MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C36D5C.68A97260" This document is a Web archive file. If you are seeing this message, this means your browser or editor doesn't support Web archive files. For more information on the Web archive format, go to http://officeupdate.microsoft.com/office/webarchive.htm ------=_NextPart_01C36D5C.68A97260 Content-Location: file:///C:/C65B91EB/COLTMABtalk.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Learning and Adaptation in Competitive and Dynamic Environment</titl= e> <!--[if gte mso 9]><xml> <o:DocumentProperties> <o:Author> shie manor</o:Author> <o:Template>Eclipse</o:Template> <o:LastAuthor>Shie Mannor</o:LastAuthor> <o:Revision>86</o:Revision> <o:TotalTime>9319</o:TotalTime> <o:Created>2003-05-03T13:31:01Z</o:Created> <o:LastSaved>2003-08-28T16:03:35Z</o:LastSaved> <o:Words>571</o:Words> <o:PresentationFormat>On-screen Show</o:PresentationFormat> <o:Company>kashya</o:Company> <o:Bytes>87688</o:Bytes> <o:Paragraphs>152</o:Paragraphs> <o:Slides>18</o:Slides> <o:Notes>1</o:Notes> <o:Version>10.2625</o:Version> </o:DocumentProperties> <o:OfficeDocumentSettings> <o:PixelsPerInch>80</o:PixelsPerInch> </o:OfficeDocumentSettings> </xml><![endif]--> <link rel=3DPresentation-XML href=3D"COLTMABtalk_files/pres.xml"> <meta name=3DDescription content=3D"8/28/2003: Lower Bounds on the Sample Complexity of Exploration = in the Multi-Armed Bandit Problem"> <meta http-equiv=3Dexpires content=3D0> <![if !ppt]><script> <!-- var ver =3D 0, appVer =3D navigator.appVersion, msie =3D appVer.indexOf( "= MSIE " ) var msieWin31 =3D (appVer.indexOf( "Windows 3.1" ) >=3D 0), isMac =3D (app= Ver.indexOf("Macintosh") >=3D 0) if( msie >=3D 0 ) ver =3D parseFloat( appVer.substring( msie+5, appVer.indexOf ( ";", msie = ) ) ) else ver =3D parseInt( appVer ) browserSupported=3D0 if( !isMac && ver >=3D 4 && msie >=3D 0 ) { browserSupported=3D1 window.location.replace( 'COLTMABtalk_files/frame.htm'+document.location.= hash ) } //--> </script> <![endif]> </head> <body> <script><!-- if( browserSupported ) document.writeln('<div style=3D"visibility:hidden">'); //--></script><font face=3DArial size=3D2><b> <p>This presentation contains content that your browser may not be able to = show properly. 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<p:placeholder type=3D"subTitle" position=3D"1"/></v:shape> <div dir=3DLTR v:shape=3D"_x0000_s2050" class=3DCT style=3D'direction:ltr'= ><span style=3D'position:absolute;top:8.5%;left:16.85%;width:87.64%;height:8.5%'>= <span lang=3DEN-US>Lower Bounds on the Sample </span></span><span style=3D'posit= ion: absolute;top:17.5%;left:16.85%;width:94.0%;height:8.5%'><span lang=3DEN-US= >Complexity of Exploration in the </span></span><span style=3D'position:absolute;top:2= 6.25%; left:16.85%;width:83.52%;height:8.5%'><span lang=3DEN-US>Multi-Armed Bandit Problem</span></span></div> <div v:shape=3D"_x0000_s2051" class=3DCB> <div dir=3DLTR style=3D'text-align:center;mso-line-spacing:"80 20 0";direc= tion: ltr;position:absolute;top:42.0%;left:19.47%;width:74.71%;height:8.25%'><sp= an lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:124%'>Shie Mannor </span></div> <div dir=3DLTR style=3D'text-align:center;mso-line-spacing:"80 20 0";direc= tion: ltr;position:absolute;top:50.0%;left:19.47%;width:74.71%;height:8.25%'><sp= an lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:124%'>John N. Tsitsiklis </span></div> <div dir=3DLTR style=3D'text-align:center;mso-line-spacing:"80 20 0";direc= tion: ltr;position:absolute;top:58.0%;left:19.47%;width:74.71%;height:5.75%'><sp= an lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:86%;display:none'> </span></div> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"80 20 0";directi= on:ltr; position:absolute;top:63.5%;left:19.47%;width:74.71%;height:5.75%'><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:86%;display:none'> </span></div> <div dir=3DLTR style=3D'text-align:center;mso-line-spacing:"80 20 0";direc= tion: ltr;position:absolute;top:69.0%;left:13.29%;width:87.07%;height:5.0%'><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:72%'>Laboratory for Information and Decision Systems </span>= </div> <div dir=3DLTR style=3D'text-align:center;mso-line-spacing:"80 20 0";direc= tion: ltr;position:absolute;top:73.75%;left:19.47%;width:74.71%;height:5.0%'><sp= an lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:72%'>Massachusetts Institute of Technology</span></div> </div> </p:slide></div> </body> </html> ------=_NextPart_01C36D5C.68A97260 Content-Location: file:///C:/C65B91EB/COLTMABtalk_files/master07_image001.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh/gH2AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAD8 AfQAgQAAAAAAAABmZpnMzAL/FI6py+0Po5y02ouz3rz7D4biSEKCUabqyrbuC8fyTJtnjef6zvf+ D3ycbsGi8YhMKperIZEJjUqn1OrLObRqt9yuV4rNfsfksvkcCovR7Lb7PVav4fS6/c6Tz/H8vv/P obcHSFhoCCg4eLjI2FiWqOgoOUmpBBlZmam5OXOJyQkaKurh+Tl6iprKUGqq6vrKydoKS1u7KDtr q7t7h5vLCxxs5vskbHyMRlyMzNyspbzsLD2dBB1NjZ29Y42i7f1Nw90NTl6eIj5urr6+gZ7ODh9v Iy5fb7/qfq9v7369//+t3zuABLMJHFgwYbODChtOO4jQoURdECNOvOiqIsaN/7YqWuQIcpPHkCRP efxYMuWtkSpbUjqJ0qVMPDBn2jQEM+bNnclq8vxpJ6dOoES3CC2KtGfOpEzjHG0K1ejTqFSnCPVX 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class=3DO style=3D'text-align:cent= er; direction:ltr;position:absolute;top:94.5%;left:35.2%;width:29.77%;height:3= .0%'><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:67%;mso-field-code:meta15'>COLT 2003</span><span style=3D'font-f= amily: Verdana;mso-ascii-font-family:Verdana;font-size:67%;mso-special-format:las= tCR; display:none'> </span></div> <p:shaperange href=3D"master06.xml#_x0000_s6154"/> <div dir=3DLTR v:shape=3D"_x0000_s6154" class=3DO style=3D'direction:ltr;p= osition: absolute;top:94.5%;left:72.65%;width:21.53%;height:3.0%'><span lang=3DAR-SA style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-bidi-font-fam= ily: Arial;font-size:67%;mso-field-code:meta16' dir=3Drtl><span dir=3Dltr></spa= n>2</span><span style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:67%; mso-special-format:lastCR;display:none'> </span></div> <![endif]><p:shaperange href=3D"master06.xml#_x0000_m6150"/><v:shape id=3D= "_x0000_s10242" 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fillcolor=3D"#3cc [4]" stroked=3D"f" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#5f5f5f [2]"/> <v:textbox style=3D'mso-fit-shape-to-text:t'/> </v:shape> <div dir=3DLTR v:shape=3D"_x0000_s10242" class=3DT style=3D'direction:ltr;= position: absolute;top:12.75%;left:15.91%;width:78.08%;height:7.75%'><span lang=3DEN= -US>Problem Definition</span></div> <div v:shape=3D"_x0000_s10243"> <div class=3DB1 style=3D'mso-margin-left-alt:588'></div> <div class=3DB2 style=3D'mso-margin-left-alt:840'></div> <div class=3DB3 style=3D'mso-margin-left-alt:1092'></div> <div class=3DB4 style=3D'mso-margin-left-alt:1380'></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-line-spacing:"100 0 = 0"; mso-margin-left-alt:348;direction:ltr;position:absolute;top:26.25%;left:14= .79%; width:80.89%;height:5.75%'><span style=3D'mso-special-format:nobullet; display:none;color:#006666;mso-color-index:3;font-family:Wingdings;font-si= ze: 70%'>£</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-asc= ii-font-family: Verdana;font-size:83%'>Given: </span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-line-spacing:"100 0 = 0"; mso-margin-left-alt:348;direction:ltr;position:absolute;top:31.5%;left:14.= 79%; width:80.89%;height:5.75%'><span style=3D'mso-special-format:nobullet; display:none;color:#006666;mso-color-index:3;font-family:Wingdings;font-si= ze: 70%'>£</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-asc= ii-font-family: Verdana;font-size:83%'>N arms. </span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-line-spacing:"100 0 = 0"; mso-margin-left-alt:348;direction:ltr;position:absolute;top:36.75%;left:14= .79%; width:84.26%;height:5.75%'><span style=3D'mso-special-format:nobullet; display:none;color:#006666;mso-color-index:3;font-family:Wingdings;font-si= ze: 70%'>£</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-asc= ii-font-family: Verdana;font-size:83%'>The reward of each arm is an IID random </span= ></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-line-spacing:"100 0 = 0"; mso-margin-left-alt:348;direction:ltr;position:absolute;top:42.25%;left:14= .79%; width:87.07%;height:5.75%'><span style=3D'mso-special-format:nobullet; display:none;color:#006666;mso-color-index:3;font-family:Wingdings;font-si= ze: 70%'>£</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-asc= ii-font-family: Verdana;font-size:83%'>variable with unknown mean and variance. </span= ></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-line-spacing:"100 0 = 0"; mso-margin-left-alt:348;direction:ltr;position:absolute;top:47.5%;left:14.= 79%; width:80.89%;height:5.75%'><span style=3D'mso-special-format:nobullet; display:none;color:#006666;mso-color-index:3;font-family:Wingdings;font-si= ze: 70%'>£</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-asc= ii-font-family: Verdana;font-size:83%;display:none'> </span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-line-spacing:"100 0 = 0"; mso-margin-left-alt:348;direction:ltr;position:absolute;top:52.75%;left:14= .79%; width:80.89%;height:5.75%'><span style=3D'mso-special-format:nobullet; display:none;color:#006666;mso-color-index:3;font-family:Wingdings;font-si= ze: 70%'>£</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-asc= ii-font-family: Verdana;font-size:83%'>Decision maker should decide after </span></di= v> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-line-spacing:"100 0 = 0"; mso-margin-left-alt:348;direction:ltr;position:absolute;top:58.25%;left:14= .79%; width:80.89%;height:5.75%'><span style=3D'mso-special-format:nobullet; display:none;color:#006666;mso-color-index:3;font-family:Wingdings;font-si= ze: 70%'>£</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-asc= ii-font-family: Verdana;font-size:83%'>some time which is the </span><span lang=3DEN-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-hansi-font-fa= mily: Arial;font-size:83%'>“</span><span lang=3DEN-US style=3D'font-family= :Verdana; mso-ascii-font-family:Verdana;font-size:83%'>best</span><span lang=3DEN-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-hansi-font-fa= mily: Arial;font-size:83%'>”</span><span lang=3DEN-US style=3D'font-family= :Verdana; mso-ascii-font-family:Verdana;font-size:83%'> arm. </span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-line-spacing:"100 0 = 0"; mso-margin-left-alt:348;direction:ltr;position:absolute;top:63.5%;left:14.= 79%; width:80.89%;height:5.75%'><span style=3D'mso-special-format:nobullet; display:none;color:#006666;mso-color-index:3;font-family:Wingdings;font-si= ze: 70%'>£</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-asc= ii-font-family: Verdana;font-size:83%;display:none'> </span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-line-spacing:"100 0 = 0"; mso-margin-left-alt:348;direction:ltr;position:absolute;top:68.75%;left:14= .79%; width:96.62%;height:5.75%'><span style=3D'mso-special-format:nobullet; display:none;color:#006666;mso-color-index:3;font-family:Wingdings;font-si= ze: 70%'>£</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-asc= ii-font-family: Verdana;font-size:83%'>We consider PAC optimal strategies </span><span lang=3DEN-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-= hansi-font-family: Arial;font-size:83%'>–</span><span lang=3DEN-US style=3D'font-family= :Verdana; mso-ascii-font-family:Verdana;font-size:83%'> strategies </span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-line-spacing:"100 0 = 0"; mso-margin-left-alt:348;direction:ltr;position:absolute;top:74.0%;left:14.= 79%; width:95.69%;height:5.75%'><span style=3D'mso-special-format:nobullet; display:none;color:#006666;mso-color-index:3;font-family:Wingdings;font-si= ze: 70%'>£</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-asc= ii-font-family: Verdana;font-size:83%'>that return an </span><span lang=3DEL style=3D'font= -family: Arial;mso-ascii-font-family:Verdana;mso-bidi-font-family:Arial;mso-hansi-f= ont-family: Verdana;font-size:83%'>ε</span><span lang=3DEN-US style=3D'font-famil= y:Verdana; mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana;font-size:83%'> optimal arm with probability at </span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-line-spacing:"100 0 = 0"; mso-margin-left-alt:348;direction:ltr;position:absolute;top:79.5%;left:14.= 79%; width:80.89%;height:5.75%'><span style=3D'mso-special-format:nobullet; display:none;color:#006666;mso-color-index:3;font-family:Wingdings;font-si= ze: 70%'>£</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-asc= ii-font-family: Verdana;mso-hansi-font-family:Verdana;font-size:83%'>least </span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:83%'><i>1- </i></span><span lang=3DEN-US style=3D'font-family:Symbol;mso-ascii-font-family:Verdana;mso= -hansi-font-family: Verdana;font-size:83%;mso-char-type:symbol'><i>d</i></span><span lang=3DEN= -US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:83%'>. </span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-line-spacing:"100 0 = 0"; mso-margin-left-alt:348;direction:ltr;position:absolute;top:84.75%;left:14= .79%; width:80.89%;height:5.75%'><span style=3D'mso-special-format:nobullet; display:none;color:#006666;mso-color-index:3;font-family:Wingdings;font-si= ze: 70%'>£</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-asc= ii-font-family: Verdana;font-size:83%;display:none'> </span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-line-spacing:"100 0 = 0"; mso-margin-left-alt:348;direction:ltr;position:absolute;top:90.0%;left:14.= 79%; width:80.89%;height:5.75%'><span style=3D'mso-special-format:nobullet; 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rel=3DOLE-Object-Data href=3Doledata.mso> <!--[if !mso]> <style> v\:* {behavior:url(#default#VML);} o\:* {behavior:url(#default#VML);} p\:* {behavior:url(#default#VML);} .shape {behavior:url(#default#VML);} v\:textbox {display:none;} </style> <![endif]--> <title>Learning and Adaptation in Competitive and Dynamic Environment</titl= e> <![if IE]> <base href=3D"file:///C:\C65B91EB\COLTMABtalk_files\slide0005.htm" id=3D"webarch_temp_base_tag"> <![endif]> <meta name=3DDescription content=3D"8/28/2003: Some History"> <link rel=3DStylesheet href=3D"master06_stylesheet.css"> <![if !ppt]> <style media=3Dprint> <!--.sld {left:0px !important; width:6.0in !important; height:4.5in !important; font-size:107% !important;} --> </style> <script src=3Dscript.js></script><script><!-- if( !IsNts() ) Redirect( "PPTSld" ); //--></script><!--[if vml]><script>g_vml =3D 1; </script><![endif]--><![endif]><p:slidetransition advancetime=3D"71168" flag=3D"1025"/><o:shapelayout v:ext=3D"edit"> <o:idmap 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direction:ltr;position:absolute;top:94.5%;left:35.2%;width:29.77%;height:3= .0%'><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:67%;mso-field-code:meta15'>COLT 2003</span><span style=3D'font-f= amily: Verdana;mso-ascii-font-family:Verdana;font-size:67%;mso-special-format:las= tCR; display:none'> </span></div> <p:shaperange href=3D"master06.xml#_x0000_s6154"/> <div v:shape=3D"_x0000_s6154" class=3DO> <div dir=3DLTR style=3D'direction:ltr;position:absolute;top:94.5%;left:72.= 65%; width:21.53%;height:3.0%'><span lang=3DAR-SA style=3D'font-family:Arial; mso-ascii-font-family:Verdana;mso-bidi-font-family:Arial;font-size:67%; mso-field-code:meta16' dir=3Drtl><span dir=3Dltr></span>3</span><span style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:67%; mso-special-format:lastCR;display:none'> </span></div> </div> <![endif]><p:shaperange href=3D"master06.xml#_x0000_m6150"/><v:shape id=3D= "_x0000_s12290" type=3D"#_x0000_m6150" style=3D'position:absolute;left:107.875pt;top:23.7= 5pt; width:575.875pt;height:90pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"title"/></v:shape><p:shaperange href=3D"master06.xml#_x0000_m6151"/><v:shape id=3D"_x0000_s12291" type=3D= "#_x0000_m6151" style=3D'position:absolute;left:107.875pt;top:143.875pt;width:575.875pt; height:324pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"body" position=3D"1"/></v:shape> <div dir=3DLTR v:shape=3D"_x0000_s12290" class=3DT style=3D'direction:ltr;= position: absolute;top:12.75%;left:15.91%;width:78.08%;height:7.75%'><span lang=3DEN= -US>Some History</span></div> <div v:shape=3D"_x0000_s12291" class=3DB> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:26.75%;left:15.91%;width:78.08%;height:5.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:83%'>= Some variants of MAB problem: </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:33.25%;left:15.91%;width:91.57%;height:5.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:86%'>Discounted, Bayesian, Markovi= an, expected </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:39.75%;left:15.91%;width:78.08%;height:5.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:86%'>reward, simultaneous (restles= s), and </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:46.5%;left:15.91%;width:78.08%;height:5.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:86%'>adversarial setups. </spa= n></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:53.25%;left:15.91%;width:78.08%;height:5.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:86%;display:none'> </span></di= v> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:59.75%;left:15.91%;width:90.44%;height:5.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:86%'>[Jennison et. al. 82</span><s= pan lang=3DEN-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-= hansi-font-family: Arial;font-size:86%'>’</span><span lang=3DEN-US style=3D'font-family= :Verdana; mso-ascii-font-family:Verdana;font-size:86%'>] and [Siegmund 85</span><span lang=3DEN-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-= hansi-font-family: Arial;font-size:86%'>’</span><span lang=3DEN-US style=3D'font-family= :Verdana; mso-ascii-font-family:Verdana;font-size:86%'>] </span><span lang=3DEN-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-hansi-font-fa= mily: Arial;font-size:86%'>–</span><span lang=3DEN-US style=3D'font-family= :Verdana; mso-ascii-font-family:Verdana;font-size:86%'> </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:66.5%;left:15.91%;width:78.08%;height:5.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:86%'>find an almost optimal arm wi= th high </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:73.25%;left:15.91%;width:78.08%;height:5.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:86%'>probability for<span style=3D'mso-spacerun:yes'>        = ;   </span>.</span></div> </div> <v:shapetype id=3D"_x0000_t75" 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href=3D"master06.xml#_x0000_s6153"/> <div dir=3DLTR v:shape=3D"_x0000_s6153" class=3DO style=3D'text-align:cent= er; direction:ltr;position:absolute;top:94.5%;left:35.2%;width:29.77%;height:3= .0%'><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:67%;mso-field-code:meta15'>COLT 2003</span><span style=3D'font-f= amily: Verdana;mso-ascii-font-family:Verdana;font-size:67%;mso-special-format:las= tCR; display:none'> </span></div> <p:shaperange href=3D"master06.xml#_x0000_s6154"/> <div v:shape=3D"_x0000_s6154" class=3DO> <div dir=3DLTR style=3D'direction:ltr;position:absolute;top:94.5%;left:72.= 65%; width:21.53%;height:3.0%'><span lang=3DAR-SA style=3D'font-family:Arial; mso-ascii-font-family:Verdana;mso-bidi-font-family:Arial;font-size:67%; mso-field-code:meta16' dir=3Drtl><span dir=3Dltr></span>4</span><span style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:67%; mso-special-format:lastCR;display:none'> </span></div> </div> <![endif]><p:shaperange href=3D"master06.xml#_x0000_m6150"/><v:shape id=3D= "_x0000_s92162" type=3D"#_x0000_m6150" style=3D'position:absolute;left:107.875pt;top:23.7= 5pt; width:575.875pt;height:90pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"title"/></v:shape><p:shaperange href=3D"master06.xml#_x0000_m6151"/><v:shape id=3D"_x0000_s92260" type=3D= "#_x0000_m6151" style=3D'position:absolute;left:107.875pt;top:143.875pt;width:575.875pt; height:324pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"body" position=3D"1"/></v:shape> <div dir=3DLTR v:shape=3D"_x0000_s92162" class=3DT style=3D'direction:ltr;= position: absolute;top:12.75%;left:15.91%;width:78.08%;height:7.75%'><span lang=3DEN= -US>The Upper Bound</span></div> <div v:shape=3D"_x0000_s92260" class=3DB> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:27.25%;left:15.91%;width:78.08%;height:6.75%'><span style=3D'position:= absolute; top:0%;left:4.79%;width:95.2%;height:100.0%'><span style=3D'mso-special-fo= rmat: bullet;color:#006666;mso-color-index:3;position:absolute;left:-5.03%; top:.39em;font-family:Wingdings;font-size:70%'>¡</span><span lang=3D= EN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana'><span style=3D'mso-spacerun:yes'> </span>A trivial Upper Bound </span><span lang=3DEN-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-= hansi-font-family: Arial'>–</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-a= scii-font-family: Verdana'> </span></span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:35.0%;left:15.91%;width:78.08%;height:6.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;display:none'> </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:42.75%;left:15.91%;width:78.08%;height:6.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;display:none'> </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr'><span style=3D'posi= tion:absolute; top:50.5%;left:19.66%;width:84.08%;height:6.75%'><span style=3D'mso-specia= l-format: bullet;color:#006666;mso-color-index:3;position:absolute;left:-4.45%; top:.39em;font-family:Wingdings;font-size:70%'>¡</span><span lang=3D= EN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana'>With some more= work </span><span lang=3DEN-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-= hansi-font-family: Arial'>–</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-a= scii-font-family: Verdana'> [Even-dar </span></span><span style=3D'position:absolute;top:57.= 0%; left:19.66%;width:74.34%;height:6.75%'><span lang=3DEN-US style=3D'font-fa= mily: Verdana;mso-ascii-font-family:Verdana'>et. al. 02</span><span lang=3DEN-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-hansi-font-fa= mily: Arial'>’</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-a= scii-font-family: Verdana'>] </span></span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:64.5%;left:15.91%;width:78.08%;height:6.75%'><span style=3D'position:a= bsolute; top:0%;left:4.79%;width:95.2%;height:100.0%'><span style=3D'visibility:hid= den'><span style=3D'mso-special-format:bullet;color:#006666;mso-color-index:3;positio= n: absolute;left:-5.03%;font-family:Wingdings;font-size:70%'>¡</span></= span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; display:none'> </span></span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:72.25%;left:15.91%;width:78.08%;height:6.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;mso-special-format:lastCR;display:none'> = ;</span></div> </div> <v:shapetype id=3D"_x0000_t75" coordsize=3D"21600,21600" o:spt=3D"75" o:preferrelative=3D"t" path=3D"m@4@5l@4@11@9@11@9@5xe" filled=3D"f" strok= ed=3D"f"> <v:stroke joinstyle=3D"miter"/> <v:formulas> <v:f eqn=3D"if lineDrawn pixelLineWidth 0"/> <v:f eqn=3D"sum @0 1 0"/> <v:f eqn=3D"sum 0 0 @1"/> <v:f eqn=3D"prod @2 1 2"/> <v:f eqn=3D"prod @3 21600 pixelWidth"/> <v:f eqn=3D"prod @3 21600 pixelHeight"/> <v:f eqn=3D"sum @0 0 1"/> <v:f eqn=3D"prod @6 1 2"/> <v:f eqn=3D"prod @7 21600 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xmlns:v=3D"urn:schemas-microsoft-com:vml" xmlns:o=3D"urn:schemas-microsoft-com:office:office" xmlns:p=3D"urn:schemas-microsoft-com:office:powerpoint" xmlns:oa=3D"urn:schemas-microsoft-com:office:activation" xmlns=3D"http://www.w3.org/TR/REC-html40"> <head> <meta http-equiv=3DContent-Type content=3D"text/html; charset=3Dus-ascii"> <meta name=3DProgId content=3DPowerPoint.Slide> <meta name=3DGenerator content=3D"Microsoft PowerPoint 10"> <link id=3DMain-File rel=3DMain-File href=3D"../COLTMABtalk.htm"> <link rel=3DPreview href=3Dpreview.wmf> <!--[if !mso]> <style> v\:* {behavior:url(#default#VML);} o\:* {behavior:url(#default#VML);} p\:* {behavior:url(#default#VML);} .shape {behavior:url(#default#VML);} v\:textbox {display:none;} </style> <![endif]--> <title>Learning and Adaptation in Competitive and Dynamic Environment</titl= e> <![if IE]> <base href=3D"file:///C:\C65B91EB\COLTMABtalk_files\slide0037.htm" id=3D"webarch_temp_base_tag"> <![endif]> <meta name=3DDescription 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colors=3D"#FFFFFF,#000000,#5F5F5F,#006666,#33CCCC,#99CCCC,#006666,#B2B2B2" masterhref=3D"master06.xml"> <p:shaperange href=3D"master06.xml#_x0000_s6145"/><![if !ppt]><p:shaperange href=3D"master06.xml#_x0000_s6146"/><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s6146,_x0000_s6147,_x0000_s6148,_x0000_s6149" src=3D"master06_image002.gif" style=3D'position:absolute;top:4.0%;left:0%; width:95.5%;height:48.0%'><![endif]><p:shaperange href=3D"master06.xml#_x0000_s6153"/> <div dir=3DLTR v:shape=3D"_x0000_s6153" class=3DO style=3D'text-align:cent= er; direction:ltr;position:absolute;top:94.5%;left:35.2%;width:29.77%;height:3= .0%'><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:67%;mso-field-code:meta15'>COLT 2003</span><span style=3D'font-f= amily: Verdana;mso-ascii-font-family:Verdana;font-size:67%;mso-special-format:las= tCR; display:none'> </span></div> <p:shaperange href=3D"master06.xml#_x0000_s6154"/> <div v:shape=3D"_x0000_s6154" class=3DO> <div dir=3DLTR style=3D'direction:ltr;position:absolute;top:94.5%;left:72.= 65%; width:21.53%;height:3.0%'><span lang=3DAR-SA style=3D'font-family:Arial; mso-ascii-font-family:Verdana;mso-bidi-font-family:Arial;font-size:67%; mso-field-code:meta16' dir=3Drtl><span dir=3Dltr></span>5</span><span style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:67%; mso-special-format:lastCR;display:none'> </span></div> </div> <![endif]><p:shaperange href=3D"master06.xml#_x0000_m6150"/><v:shape id=3D= "_x0000_s100354" type=3D"#_x0000_m6150" style=3D'position:absolute;left:107.875pt;top:23.7= 5pt; width:575.875pt;height:90pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"title"/></v:shape><v:rect id=3D"_x0000_s100355" st= yle=3D'position:absolute; left:99.125pt;top:150.875pt;width:595.375pt;height:334.625pt' filled=3D"f" fillcolor=3D"#3cc [4]" stroked=3D"f" strokecolor=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#5f5f5f [2]"/> </v:rect> <div dir=3DLTR v:shape=3D"_x0000_s100354" class=3DT style=3D'direction:ltr= ;position: absolute;top:12.75%;left:15.91%;width:78.08%;height:7.75%'><span lang=3DEN= -US>The Coin Setup</span></div> <div v:shape=3D"_x0000_s100355" class=3DB> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:28.5%;left:14.79%;width:80.89%;height:5.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:83%'>N coins </span><span lang=3DE= N-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-hansi-font-fa= mily: Arial;font-size:83%'>–</span><span lang=3DEN-US style=3D'font-family= :Verdana; mso-ascii-font-family:Verdana;font-size:83%'> 0/1. </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:35.0%;left:14.79%;width:91.01%;height:5.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:83%'>Each coin is a Bernoulli rand= om variable with </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:41.25%;left:14.79%;width:94.75%;height:5.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:83%'>probability </span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:83%'><i>p</i></span><span lang=3DEN-US style=3D'font-family:Verd= ana; mso-ascii-font-family:Verdana;font-size:55%;position:relative;top:.37em; mso-text-raise:-25%'><i>i</i></span><span lang=3DEN-US style=3D'font-famil= y:Verdana; mso-ascii-font-family:Verdana;font-size:83%'><span style=3D'mso-spacerun:yes'> </span>of getting </span><span lang=3DEN-= US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-hansi-font-fa= mily: Arial;font-size:83%'>“</span><span lang=3DEN-US style=3D'font-family= :Verdana; mso-ascii-font-family:Verdana;font-size:83%'>1</span><span lang=3DEN-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-hansi-font-fa= mily: Arial;font-size:83%'>”</span><span lang=3DEN-US style=3D'font-family= :Verdana; mso-ascii-font-family:Verdana;font-size:83%'> and </span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:83%'>= <i>1 - p</i></span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font= -family: Verdana;font-size:55%;position:relative;top:.37em;mso-text-raise:-25%'><i>= i </i></span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:83%'>of getting </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:47.75%;left:14.79%;width:80.89%;height:5.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Arial; mso-ascii-font-family:Verdana;mso-hansi-font-family:Arial;font-size:83%'>&= #8220;</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:83%'>0</span><span lang=3DEN-US style=3D'font-family:Arial;mso-a= scii-font-family: Verdana;mso-hansi-font-family:Arial;font-size:83%'>”</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:83%'>. </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:54.0%;left:14.79%;width:80.89%;height:5.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:83%;display:none'> </span></di= v> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:60.5%;left:14.79%;width:80.89%;height:5.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:83%'>A policy is a mapping from histories to </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:67.0%;left:14.79%;width:87.07%;height:5.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:83%'>coin selection and eventually= a termination </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:73.25%;left:14.79%;width:80.89%;height:5.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:83%'>declaring </span><span lang=3DEN-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-= hansi-font-family: Arial;font-size:83%'>“</span><span lang=3DEN-US style=3D'font-family= :Verdana; mso-ascii-font-family:Verdana;font-size:83%'>coin I is the best coin</span= ><span lang=3DEN-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-= hansi-font-family: Arial;font-size:83%'>”</span><span lang=3DEN-US style=3D'font-family= :Verdana; mso-ascii-font-family:Verdana;font-size:83%'>. </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:79.75%;left:14.79%;width:80.89%;height:5.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:83%;display:none'> </span></di= v> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:86.0%;left:14.79%;width:80.89%;height:5.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:83%;mso-special-format:lastCR; display:none'> </span></div> </div> </p:slide></div> </body> </html> ------=_NextPart_01C36D5C.68A97260 Content-Location: file:///C:/C65B91EB/COLTMABtalk_files/slide0039.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" <html xmlns:v=3D"urn:schemas-microsoft-com:vml" 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href=3D"master06_stylesheet.css"> <![if !ppt]> <style media=3Dprint> <!--.sld {left:0px !important; width:6.0in !important; height:4.5in !important; font-size:107% !important;} --> </style> <script src=3Dscript.js></script><script><!-- if( !IsNts() ) Redirect( "PPTSld" ); //--></script><!--[if vml]><script>g_vml =3D 1; </script><![endif]--><![endif]><p:slidetransition advancetime=3D"43632" flag=3D"1025"/><o:shapelayout v:ext=3D"edit"> <o:idmap v:ext=3D"edit" data=3D"117"/> </o:shapelayout> </head> <body lang=3DEN-US style=3D'margin:0px;background-color:black' onclick=3D"DocumentOnClick()" onresize=3D"_RSW()" onload=3D"LoadSld()" onkeypress=3D"_KPH()"> <div id=3DSlideObj class=3Dsld style=3D'position:absolute;top:0px;left:0px; width:534px;height:400px;font-size:16px;background-color:white;clip:rect(0%= , 101%, 101%, 0%); visibility:hidden'><p:slide coordsize=3D"720,540" colors=3D"#FFFFFF,#000000,#5F5F5F,#006666,#33CCCC,#99CCCC,#006666,#B2B2B2" masterhref=3D"master06.xml"> <p:shaperange href=3D"master06.xml#_x0000_s6145"/><![if !ppt]><p:shaperange href=3D"master06.xml#_x0000_s6146"/><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s6146,_x0000_s6147,_x0000_s6148,_x0000_s6149" src=3D"master06_image002.gif" style=3D'position:absolute;top:4.0%;left:0%; width:95.5%;height:48.0%'><![endif]><p:shaperange href=3D"master06.xml#_x0000_s6153"/> <div dir=3DLTR v:shape=3D"_x0000_s6153" class=3DO style=3D'text-align:cent= er; direction:ltr;position:absolute;top:94.5%;left:35.2%;width:29.77%;height:3= .0%'><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:67%;mso-field-code:meta15'>COLT 2003</span><span style=3D'font-f= amily: Verdana;mso-ascii-font-family:Verdana;font-size:67%;mso-special-format:las= tCR; display:none'> </span></div> <p:shaperange href=3D"master06.xml#_x0000_s6154"/> <div v:shape=3D"_x0000_s6154" class=3DO> <div dir=3DLTR style=3D'direction:ltr;position:absolute;top:94.5%;left:72.= 65%; width:21.53%;height:3.0%'><span lang=3DAR-SA style=3D'font-family:Arial; mso-ascii-font-family:Verdana;mso-bidi-font-family:Arial;font-size:67%; mso-field-code:meta16' dir=3Drtl><span dir=3Dltr></span>6</span><span style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:67%; mso-special-format:lastCR;display:none'> </span></div> </div> <![endif]><p:shaperange href=3D"master06.xml#_x0000_m6150"/><v:shape id=3D= "_x0000_s119810" type=3D"#_x0000_m6150" style=3D'position:absolute;left:107.875pt;top:23.7= 5pt; width:575.875pt;height:90pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"title"/></v:shape><p:shaperange href=3D"master06.xml#_x0000_m6151"/><v:shape id=3D"_x0000_s119811" type= =3D"#_x0000_m6151" style=3D'position:absolute;left:107.875pt;top:143.875pt;width:575.875pt; height:324pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"body" position=3D"1"/></v:shape> <div dir=3DRTL v:shape=3D"_x0000_s119810" class=3DT style=3D'position:abso= lute; top:12.75%;left:15.91%;width:78.08%;height:7.75%'><span lang=3DEN-US dir= =3Dltr>Objective</span></div> <div v:shape=3D"_x0000_s119811"> <div class=3DB1 style=3D'mso-margin-left-alt:588'></div> <div class=3DB2 style=3D'mso-margin-left-alt:840'></div> <div class=3DB3 style=3D'mso-margin-left-alt:1092'></div> <div class=3DB4 style=3D'mso-margin-left-alt:1380'></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-margin-left-alt:348; direction:ltr;position:absolute;top:27.25%;left:15.91%;width:78.08%; height:6.75%'><span style=3D'mso-special-format:nobullet;display:none; color:#006666;mso-color-index:3;font-family:Wingdings;font-size:70%'>&iexc= l;</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana'>A strategy is </span><span lang=3DEL style=3D'font-family:Arial;mso-ascii-fo= nt-family: Verdana;mso-bidi-font-family:Arial;mso-hansi-font-family:Verdana;font-size: 97%'>ε</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-asci= i-font-family: Verdana;mso-hansi-font-family:Verdana;font-size:97%'>-</span><span lang=3D= EN-US style=3D'font-family:Symbol;mso-ascii-font-family:Verdana;mso-hansi-font-f= amily: Verdana;font-size:97%;mso-char-type:symbol'>d</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:97%'> correct if: </span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-margin-left-alt:348; direction:ltr;position:absolute;top:35.0%;left:15.91%;width:78.08%;height: 6.5%'><span style=3D'position:absolute;top:0%;left:7.91%;width:92.32%; height:100.0%'><span style=3D'font-size:97%'><span style=3D'mso-special-fo= rmat: "numbullet3\,1";color:#006666;mso-color-index:3;position:absolute;left:-8.= 57%; top:.39em;font-size:70%'>1.</span></span><span lang=3DEN-US style=3D'font-= family: Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana; font-size:97%'>It terminates w.p.1 </span></span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-margin-left-alt:348; direction:ltr'><span style=3D'position:absolute;top:42.5%;left:22.09%; width:86.32%;height:6.5%'><span style=3D'font-size:97%'><span style=3D'mso= -special-format: "numbullet3\,1";color:#006666;mso-color-index:3;position:absolute;left:-7.= 15%; top:.39em;font-size:70%'>2.</span></span><span lang=3DEN-US style=3D'font-= family: Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana; font-size:97%'>For </span><span lang=3DEN-US style=3D'font-family:Verdana; mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana;font-size:97%; color:red'>any</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-a= scii-font-family: Verdana;mso-hansi-font-family:Verdana;font-size:97%'> set of coins, the co= in chosen </span></span><span style=3D'position:absolute;top:48.75%;left:22.0= 9%; width:76.21%;height:6.5%'><span lang=3DEN-US style=3D'font-family:Verdana; mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana;font-size:97%'= >is at most </span><span lang=3DEL style=3D'font-family:Arial;mso-ascii-font-f= amily: Verdana;mso-bidi-font-family:Arial;mso-hansi-font-family:Verdana;font-size: 97%'>ε</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-asci= i-font-family: Verdana;mso-hansi-font-family:Verdana;font-size:97%'>-worse than the best = </span></span><span style=3D'position:absolute;top:54.75%;left:22.09%;width:72.09%;height:6.5%= '><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:97%'>coin w.p. at least 1- </span>= <span lang=3DEN-US style=3D'font-family:Symbol;mso-ascii-font-family:Verdana;mso= -hansi-font-family: Verdana;font-size:97%;mso-char-type:symbol'>d</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:97%'>. </span></span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-margin-left-alt:348; direction:ltr;position:absolute;top:62.25%;left:15.91%;width:78.08%; height:6.5%'><span style=3D'position:absolute;top:0%;left:7.91%;width:92.3= 2%; height:100.0%'><span style=3D'font-size:97%;visibility:hidden'><span style=3D'mso-special-format:"numbullet3\,1";color:#006666;mso-color-index:= 3; position:absolute;left:-8.57%;font-size:70%'>3.</span></span><span lang=3D= EN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:97%;display:none'> </span></span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-margin-left-alt:348; direction:ltr;position:absolute;top:69.75%;left:15.91%;width:78.65%; height:6.5%'><span style=3D'mso-special-format:nobullet;display:none;color= :#006666; mso-color-index:3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:97%'>We look for a lower bound on = the </span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-margin-left-alt:348; direction:ltr;position:absolute;top:77.25%;left:15.91%;width:78.08%; height:6.5%'><span style=3D'mso-special-format:nobullet;display:none;color= :#006666; mso-color-index:3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:97%;color:red'>expected</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:97%'> number of arms pulls.</span>= </div> </div> </p:slide></div> </body> </html> ------=_NextPart_01C36D5C.68A97260 Content-Location: file:///C:/C65B91EB/COLTMABtalk_files/slide0040.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" <html xmlns:v=3D"urn:schemas-microsoft-com:vml" xmlns:o=3D"urn:schemas-microsoft-com:office:office" xmlns:p=3D"urn:schemas-microsoft-com:office:powerpoint" xmlns:oa=3D"urn:schemas-microsoft-com:office:activation" xmlns=3D"http://www.w3.org/TR/REC-html40"> <head> <meta http-equiv=3DContent-Type content=3D"text/html; charset=3Dus-ascii"> <meta name=3DProgId content=3DPowerPoint.Slide> <meta name=3DGenerator content=3D"Microsoft PowerPoint 10"> <link id=3DMain-File rel=3DMain-File href=3D"../COLTMABtalk.htm"> <link rel=3DPreview href=3Dpreview.wmf> <!--[if !mso]> <style> v\:* {behavior:url(#default#VML);} o\:* {behavior:url(#default#VML);} p\:* {behavior:url(#default#VML);} .shape {behavior:url(#default#VML);} v\:textbox {display:none;} </style> <![endif]--> <title>Learning and Adaptation in Competitive and Dynamic Environment</titl= e> <![if IE]> <base href=3D"file:///C:\C65B91EB\COLTMABtalk_files\slide0040.htm" id=3D"webarch_temp_base_tag"> <![endif]> <meta name=3DDescription content=3D"8/28/2003: What can go wrong?"> <link rel=3DStylesheet href=3D"master06_stylesheet.css"> <![if !ppt]> <style media=3Dprint> <!--.sld {left:0px !important; width:6.0in !important; height:4.5in !important; font-size:107% !important;} --> </style> <script src=3Dscript.js></script><script><!-- if( !IsNts() ) Redirect( "PPTSld" ); //--></script><!--[if vml]><script>g_vml =3D 1; </script><![endif]--><![endif]><p:slidetransition advancetime=3D"108144" flag=3D"1025"/><o:shapelayout v:ext=3D"edit"> <o:idmap v:ext=3D"edit" data=3D"118"/> </o:shapelayout> </head> <body lang=3DEN-US style=3D'margin:0px;background-color:black' onclick=3D"DocumentOnClick()" onresize=3D"_RSW()" onload=3D"LoadSld()" onkeypress=3D"_KPH()"> <div id=3DSlideObj class=3Dsld style=3D'position:absolute;top:0px;left:0px; width:534px;height:400px;font-size:16px;background-color:white;clip:rect(0%= , 101%, 101%, 0%); visibility:hidden'><p:slide coordsize=3D"720,540" colors=3D"#FFFFFF,#000000,#5F5F5F,#006666,#33CCCC,#99CCCC,#006666,#B2B2B2" masterhref=3D"master06.xml"> <p:shaperange href=3D"master06.xml#_x0000_s6145"/><![if !ppt]><p:shaperange href=3D"master06.xml#_x0000_s6146"/><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s6146,_x0000_s6147,_x0000_s6148,_x0000_s6149" src=3D"master06_image002.gif" style=3D'position:absolute;top:4.0%;left:0%; width:95.5%;height:48.0%'><![endif]><p:shaperange href=3D"master06.xml#_x0000_s6153"/> <div dir=3DLTR v:shape=3D"_x0000_s6153" class=3DO style=3D'text-align:cent= er; direction:ltr;position:absolute;top:94.5%;left:35.2%;width:29.77%;height:3= .0%'><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:67%;mso-field-code:meta15'>COLT 2003</span><span style=3D'font-f= amily: Verdana;mso-ascii-font-family:Verdana;font-size:67%;mso-special-format:las= tCR; display:none'> </span></div> <p:shaperange href=3D"master06.xml#_x0000_s6154"/> <div v:shape=3D"_x0000_s6154" class=3DO> <div dir=3DLTR style=3D'direction:ltr;position:absolute;top:94.5%;left:72.= 65%; width:21.53%;height:3.0%'><span lang=3DAR-SA style=3D'font-family:Arial; mso-ascii-font-family:Verdana;mso-bidi-font-family:Arial;font-size:67%; mso-field-code:meta16' dir=3Drtl><span dir=3Dltr></span>7</span><span style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:67%; mso-special-format:lastCR;display:none'> </span></div> </div> <![endif]><p:shaperange href=3D"master06.xml#_x0000_m6150"/><v:shape id=3D= "_x0000_s120834" type=3D"#_x0000_m6150" style=3D'position:absolute;left:107.875pt;top:23.7= 5pt; width:575.875pt;height:90pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"title"/></v:shape><p:shaperange href=3D"master06.xml#_x0000_m6151"/><v:shape id=3D"_x0000_s120835" type= =3D"#_x0000_m6151" style=3D'position:absolute;left:107.875pt;top:143.875pt;width:575.875pt; height:324pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"body" position=3D"1"/></v:shape> <div dir=3DRTL v:shape=3D"_x0000_s120834" class=3DT style=3D'position:abso= lute; top:12.75%;left:15.91%;width:78.08%;height:7.75%'><span lang=3DEN-US dir= =3Dltr>What can go wrong?</span></div> <div v:shape=3D"_x0000_s120835" class=3DB> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:27.25%;left:15.91%;width:78.08%;height:5.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:86%'>Super-smart strategy. </s= pan></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:34.0%;left:15.91%;width:78.08%;height:5.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:86%;display:none'> </span></di= v> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:40.5%;left:15.91%;width:78.08%;height:5.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:86%'>Dependence in N for N large.&= #13;</span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:47.25%;left:15.91%;width:78.08%;height:5.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:86%;display:none'> </span></di= v> <div dir=3DLTR style=3D'text-align:left;direction:ltr'><span style=3D'posi= tion:absolute; top:54.0%;left:15.91%;width:85.95%;height:5.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:86%'>Dependence in </span><span lang=3DEL style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-bid= i-font-family: Arial;mso-hansi-font-family:Verdana;font-size:83%'>ε</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:83%'> and </span><span lang=3DEN-US style=3D'font-family:Symbol;mso-ascii-font-family:Verdana;mso-hansi-font-f= amily: Verdana;font-size:83%;mso-char-type:symbol'>d</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:83%'> are expected to be </span></span><span style=3D'position:absolute;top:59.5%;left:19.66%;width:74.34%;height:5.75%= '><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:83%'>1/</span><span lang=3DEL style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-bidi-font-fam= ily: Arial;mso-hansi-font-family:Verdana;font-size:83%'>ε</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:55%;position:relative;top:-.45em; mso-text-raise:30%'>2</span><span lang=3DEN-US style=3D'font-family:Verdan= a; mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana;font-size:83%'= ><span style=3D'mso-spacerun:yes'>  </span>and<span style=3D'mso-spacerun:yes'>  </span>log(1/</span><span lang=3DEN-US style=3D'font-family:Symbol;mso-ascii-font-family:Verdana;mso-hansi-font-f= amily: Verdana;font-size:83%;mso-char-type:symbol'>d</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:83%'> ). </span></span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:66.0%;left:15.91%;width:78.08%;height:5.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana;font-size:83%; display:none'> </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr'><span style=3D'posi= tion:absolute; top:72.25%;left:15.91%;width:78.27%;height:5.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana;font-size:83%'= >Two coins – </span><span lang=3DEN-US style=3D'font-family:Verdana;mso-a= scii-font-family: Verdana;mso-hansi-font-family:Verdana;font-size:83%'>log(1/</span><span lang=3DEN-US style=3D'font-family:Symbol;mso-ascii-font-family:Verdana;mso= -hansi-font-family: Verdana;font-size:83%;mso-char-type:symbol'>d</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:83%'>) / </span><span lang=3DEL style=3D'font-family:Ari= al; mso-ascii-font-family:Verdana;mso-bidi-font-family:Arial;mso-hansi-font-fa= mily: Verdana;font-size:83%'>ε</span><span lang=3DEN-US style=3D'font-famil= y:Verdana; mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana;font-size:55%; position:relative;top:-.45em;mso-text-raise:30%'>2</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:83%'><span style=3D'mso-spacerun:yes'> </span>[Anth= ony and </span></span><span style=3D'position:absolute;top:77.5%;left:19.66%; width:74.34%;height:5.75%'><span lang=3DEN-US style=3D'font-family:Verdana; mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana;font-size:83%'= >Bartlett 99’].</span></span></div> </div> </p:slide></div> </body> </html> ------=_NextPart_01C36D5C.68A97260 Content-Location: file:///C:/C65B91EB/COLTMABtalk_files/slide0038.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" <html xmlns:v=3D"urn:schemas-microsoft-com:vml" xmlns:o=3D"urn:schemas-microsoft-com:office:office" xmlns:p=3D"urn:schemas-microsoft-com:office:powerpoint" xmlns:oa=3D"urn:schemas-microsoft-com:office:activation" xmlns=3D"http://www.w3.org/TR/REC-html40"> <head> <meta http-equiv=3DContent-Type content=3D"text/html; charset=3Dus-ascii"> <meta name=3DProgId content=3DPowerPoint.Slide> <meta name=3DGenerator content=3D"Microsoft PowerPoint 10"> <link id=3DMain-File rel=3DMain-File href=3D"../COLTMABtalk.htm"> <link rel=3DPreview href=3Dpreview.wmf> <link rel=3DOLE-Object-Data href=3Doledata.mso> <!--[if !mso]> <style> v\:* {behavior:url(#default#VML);} o\:* {behavior:url(#default#VML);} p\:* {behavior:url(#default#VML);} .shape {behavior:url(#default#VML);} v\:textbox {display:none;} </style> <![endif]--> <title>Learning and Adaptation in Competitive and Dynamic Environment</titl= e> <![if IE]> <base href=3D"file:///C:\C65B91EB\COLTMABtalk_files\slide0038.htm" id=3D"webarch_temp_base_tag"> <![endif]> <meta name=3DDescription content=3D"8/28/2003: The Main Result"> <link rel=3DStylesheet href=3D"master06_stylesheet.css"> <![if !ppt]> <style media=3Dprint> <!--.sld {left:0px !important; width:6.0in !important; height:4.5in !important; font-size:107% !important;} --> </style> <script src=3Dscript.js></script><script><!-- if( !IsNts() ) Redirect( "PPTSld" ); //--></script><!--[if vml]><script>g_vml =3D 1; </script><![endif]--><![endif]><p:slidetransition advancetime=3D"87776" flag=3D"1025"/><o:shapelayout v:ext=3D"edit"> <o:idmap v:ext=3D"edit" data=3D"116"/> </o:shapelayout> </head> <body lang=3DEN-US style=3D'margin:0px;background-color:black' onclick=3D"DocumentOnClick()" onresize=3D"_RSW()" onload=3D"LoadSld()" onkeypress=3D"_KPH()"> <div id=3DSlideObj class=3Dsld style=3D'position:absolute;top:0px;left:0px; width:534px;height:400px;font-size:16px;background-color:white;clip:rect(0%= , 101%, 101%, 0%); visibility:hidden'><p:slide coordsize=3D"720,540" colors=3D"#FFFFFF,#000000,#5F5F5F,#006666,#33CCCC,#99CCCC,#006666,#B2B2B2" masterhref=3D"master06.xml"> <p:shaperange href=3D"master06.xml#_x0000_s6145"/><![if !ppt]><p:shaperange href=3D"master06.xml#_x0000_s6146"/><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s6146,_x0000_s6147,_x0000_s6148,_x0000_s6149" src=3D"master06_image002.gif" style=3D'position:absolute;top:4.0%;left:0%; width:95.5%;height:48.0%'><![endif]><p:shaperange href=3D"master06.xml#_x0000_s6153"/> <div dir=3DLTR v:shape=3D"_x0000_s6153" class=3DO style=3D'text-align:cent= er; direction:ltr;position:absolute;top:94.5%;left:35.2%;width:29.77%;height:3= .0%'><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:67%;mso-field-code:meta15'>COLT 2003</span><span style=3D'font-f= amily: Verdana;mso-ascii-font-family:Verdana;font-size:67%;mso-special-format:las= tCR; display:none'> </span></div> <p:shaperange href=3D"master06.xml#_x0000_s6154"/> <div v:shape=3D"_x0000_s6154" class=3DO> <div dir=3DLTR style=3D'direction:ltr;position:absolute;top:94.5%;left:72.= 65%; width:21.53%;height:3.0%'><span lang=3DAR-SA style=3D'font-family:Arial; mso-ascii-font-family:Verdana;mso-bidi-font-family:Arial;font-size:67%; mso-field-code:meta16' dir=3Drtl><span dir=3Dltr></span>8</span><span style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:67%; mso-special-format:lastCR;display:none'> </span></div> </div> <![endif]><p:shaperange href=3D"master06.xml#_x0000_m6150"/><v:shape id=3D= "_x0000_s118786" type=3D"#_x0000_m6150" style=3D'position:absolute;left:107.875pt;top:23.7= 5pt; width:575.875pt;height:90pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"title"/></v:shape><p:shaperange href=3D"master06.xml#_x0000_m6151"/><v:shape id=3D"_x0000_s118787" type= =3D"#_x0000_m6151" style=3D'position:absolute;left:107.875pt;top:143.875pt;width:575.875pt; height:154.5pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"body" position=3D"1"/></v:shape> <div dir=3DRTL v:shape=3D"_x0000_s118786" class=3DT style=3D'position:abso= lute; top:12.75%;left:15.91%;width:78.08%;height:7.75%'><span lang=3DEN-US dir= =3Dltr>The Main Result</span></div> <div v:shape=3D"_x0000_s118787" class=3DB> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:26.75%;left:15.91%;width:79.21%;height:6.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana'>There exists a collection of coins </span></div> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:33.75%;left:15.91%;width:82.39%;height:6.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana'><i><span style=3D'mso-tab-count:2;width:12.13%'> </span>p</i></span><span lang=3DEN= -US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:66%; position:relative;top:.37em;mso-text-raise:-25%'><i>1</i></span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana'><= i><span style=3D'mso-spacerun:yes'> </span>=3D </i></span><span lang=3DEN-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-hansi-font-fa= mily: Arial'><i>½</i></span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana'><i> + </i></span><span lang=3DEL style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-bidi-font-fam= ily: Arial;mso-hansi-font-family:Verdana;font-size:97%'><i>ε</i></span><sp= an lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:97%'><i>, p</i></span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:66%;position:relative;top:.37em; mso-text-raise:-25%'><i>2</i></span><span lang=3DEN-US style=3D'font-famil= y:Verdana; mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana;font-size:97%'= ><i>=3D ½ ,…, p</i></span><span lang=3DEN-US style=3D'font-family:Ver= dana; mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana;font-size:66%; position:relative;top:.37em;mso-text-raise:-25%'><i>N</i></span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:97%'><i>=3D ½</i></span><sp= an lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:97%'> </span></div> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:40.75%;left:15.91%;width:78.08%;height:6.5%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:97%'>such that every </span><span lang=3DEL style=3D'fon= t-family: Arial;mso-ascii-font-family:Verdana;mso-bidi-font-family:Arial;mso-hansi-f= ont-family: Verdana;font-size:97%'>ε</span><span lang=3DEN-US style=3D'font-famil= y:Verdana; mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana;font-size:97%'= >-</span><span lang=3DEN-US style=3D'font-family:Symbol;mso-ascii-font-family:Verdana;mso= -hansi-font-family: Verdana;font-size:97%;mso-char-type:symbol'>d</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:97%'> correct policy </span></div> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:47.75%;left:15.91%;width:78.08%;height:6.5%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:97%'>satisfies (<span style=3D'mso-spacerun:yes'>        = ;        </span>) </span></div> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:54.5%;left:15.91%;width:78.08%;height:6.5%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:97%;display:none'> </span></div> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:61.5%;left:15.91%;width:78.08%;height:6.5%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: 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nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana'>Result is proven even under the </span= ></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:77.0%;left:16.29%;width:89.7%;height:6.75%'><span style=3D'mso-special= -format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana'>assumption that the coins biases are <= /span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:84.75%;left:16.29%;width:82.95%;height:6.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana'>known (permutation is 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xmlns:p=3D"urn:schemas-microsoft-com:office:powerpoint" xmlns:oa=3D"urn:schemas-microsoft-com:office:activation" xmlns=3D"http://www.w3.org/TR/REC-html40"> <head> <meta http-equiv=3DContent-Type content=3D"text/html; charset=3Dus-ascii"> <meta name=3DProgId content=3DPowerPoint.Slide> <meta name=3DGenerator content=3D"Microsoft PowerPoint 10"> <link id=3DMain-File rel=3DMain-File href=3D"../COLTMABtalk.htm"> <link rel=3DPreview href=3Dpreview.wmf> <link rel=3DOLE-Object-Data href=3Doledata.mso> <!--[if !mso]> <style> v\:* {behavior:url(#default#VML);} o\:* {behavior:url(#default#VML);} p\:* {behavior:url(#default#VML);} .shape {behavior:url(#default#VML);} v\:textbox {display:none;} </style> <![endif]--> <title>Learning and Adaptation in Competitive and Dynamic Environment</titl= e> <![if IE]> <base href=3D"file:///C:\C65B91EB\COLTMABtalk_files\slide0006.htm" id=3D"webarch_temp_base_tag"> <![endif]> <meta name=3DDescription content=3D"8/28/2003: Proof"> <link rel=3DStylesheet href=3D"master06_stylesheet.css"> <![if !ppt]> <style media=3Dprint> <!--.sld {left:0px !important; width:6.0in !important; height:4.5in !important; font-size:107% !important;} --> </style> <script src=3Dscript.js></script><script><!-- if( !IsNts() ) Redirect( "PPTSld" ); //--></script><!--[if vml]><script>g_vml =3D 1; </script><![endif]--><![endif]><p:slidetransition advancetime=3D"45856" flag=3D"1025"/><o:shapelayout v:ext=3D"edit"> <o:idmap v:ext=3D"edit" data=3D"13"/> </o:shapelayout> </head> <body lang=3DEN-US style=3D'margin:0px;background-color:black' onclick=3D"DocumentOnClick()" onresize=3D"_RSW()" onload=3D"LoadSld()" onkeypress=3D"_KPH()"> <div id=3DSlideObj class=3Dsld style=3D'position:absolute;top:0px;left:0px; width:534px;height:400px;font-size:16px;background-color:white;clip:rect(0%= , 101%, 101%, 0%); visibility:hidden'><p:slide coordsize=3D"720,540" colors=3D"#FFFFFF,#000000,#5F5F5F,#006666,#33CCCC,#99CCCC,#006666,#B2B2B2" masterhref=3D"master06.xml"> <p:shaperange href=3D"master06.xml#_x0000_s6145"/><![if !ppt]><p:shaperange href=3D"master06.xml#_x0000_s6146"/><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s6146,_x0000_s6147,_x0000_s6148,_x0000_s6149" src=3D"master06_image002.gif" style=3D'position:absolute;top:4.0%;left:0%; width:95.5%;height:48.0%'><![endif]><p:shaperange href=3D"master06.xml#_x0000_s6153"/> <div dir=3DLTR v:shape=3D"_x0000_s6153" class=3DO style=3D'text-align:cent= er; direction:ltr;position:absolute;top:94.5%;left:35.2%;width:29.77%;height:3= .0%'><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:67%;mso-field-code:meta15'>COLT 2003</span><span style=3D'font-f= amily: Verdana;mso-ascii-font-family:Verdana;font-size:67%;mso-special-format:las= tCR; display:none'> </span></div> <p:shaperange href=3D"master06.xml#_x0000_s6154"/> <div v:shape=3D"_x0000_s6154" class=3DO> <div dir=3DLTR style=3D'direction:ltr;position:absolute;top:94.5%;left:72.= 65%; width:21.53%;height:3.0%'><span lang=3DAR-SA style=3D'font-family:Arial; mso-ascii-font-family:Verdana;mso-bidi-font-family:Arial;font-size:67%; mso-field-code:meta16' dir=3Drtl><span dir=3Dltr></span>9</span><span style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:67%; mso-special-format:lastCR;display:none'> </span></div> </div> <![endif]><p:shaperange href=3D"master06.xml#_x0000_m6150"/><v:shape id=3D= "_x0000_s13314" type=3D"#_x0000_m6150" style=3D'position:absolute;left:107.875pt;top:23.7= 5pt; width:575.875pt;height:90pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"title"/></v:shape><p:shaperange href=3D"master06.xml#_x0000_m6151"/><v:shape id=3D"_x0000_s13315" type=3D= "#_x0000_m6151" style=3D'position:absolute;left:98.625pt;top:143.875pt;width:601.625pt; height:324pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"body" position=3D"1"/></v:shape> <div dir=3DLTR v:shape=3D"_x0000_s13314" class=3DT style=3D'direction:ltr;= position: absolute;top:12.75%;left:15.91%;width:78.08%;height:7.75%'><span lang=3DEN= -US>Proof</span></div> <div v:shape=3D"_x0000_s13315"> <div class=3DB1 style=3D'mso-margin-left-alt:588'></div> <div class=3DB2 style=3D'mso-margin-left-alt:840'></div> <div class=3DB3 style=3D'mso-margin-left-alt:1092'></div> <div class=3DB4 style=3D'mso-margin-left-alt:1380'></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-margin-left-alt:348; direction:ltr;position:absolute;top:27.25%;left:14.79%;width:81.64%; height:6.75%'><span style=3D'mso-special-format:nobullet;display:none; color:#006666;mso-color-index:3;font-family:Wingdings;font-size:70%'>&iexc= l;</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana'>D= efine hypotheses </span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-margin-left-alt:348; direction:ltr;position:absolute;top:35.0%;left:14.79%;width:93.07%;height: 6.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#0066= 66; mso-color-index:3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana'><= span style=3D'mso-spacerun:yes'>   </span></span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana'><i>H</i></span= ><span lang=3DEN-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-= bidi-font-family: Arial;mso-hansi-font-family:Verdana;font-size:66%;position:relative; top:.37em;mso-text-raise:-25%'><i>ℓ</i></span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana'><i><span style=3D'mso-spacerun:yes'> </span>:<span style=3D'mso-spacerun:yes'>     </span>p</i></span><sp= an lang=3DEN-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-= bidi-font-family: Arial;mso-hansi-font-family:Verdana;font-size:66%;position:relative; top:.37em;mso-text-raise:-25%'><i>ℓ</i></span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana'><i>=3D</i></sp= an><span lang=3DEN-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-= hansi-font-family: Arial'><i>½</i></span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana'><i>+</i></span><span lang=3DEL style=3D'fon= t-family: Arial;mso-ascii-font-family:Verdana;mso-bidi-font-family:Arial;mso-hansi-f= ont-family: Verdana;font-size:97%'><i>ε</i></span><span lang=3DEN-US style=3D'fon= t-family: Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana; font-size:97%'><i><span style=3D'mso-spacerun:yes'>   </span>;<s= pan style=3D'mso-spacerun:yes'>     </span>p</i></span><sp= an lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:66%;position:relative;top:.37em; mso-text-raise:-25%'><i>m</i></span><span lang=3DEN-US style=3D'font-famil= y:Verdana; mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana;font-size:97%'= ><i><span style=3D'mso-spacerun:yes'> </span>=3D </i></span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:97%'><i>½</i></span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:97%'><i><span style=3D'mso-spacerun:yes'>  </span>(= m </i></span><span lang=3DEN-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-= bidi-font-family: Arial;mso-hansi-font-family:Verdana;font-size:97%'><i>≠</i></span><s= pan lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:97%'><i> </i></span><span lang=3DE= N-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-bidi-font-fam= ily: Arial;mso-hansi-font-family:Verdana'><i>ℓ</i></span><span lang=3DEN-= US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:97%'><i>) </i></span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-margin-left-alt:348; direction:ltr;position:absolute;top:42.75%;left:14.79%;width:81.64%; height:6.5%'><span style=3D'mso-special-format:nobullet;display:none;color= :#006666; mso-color-index:3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:97%;display:none'><i> </i></sp= an></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-margin-left-alt:348; direction:ltr'><span style=3D'position:absolute;top:50.25%;left:14.79%; width:82.77%;height:6.5%'><span style=3D'mso-special-format:nobullet;displ= ay: none;color:#006666;mso-color-index:3;font-family:Wingdings;font-size:70%'>= ¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:97%'><span style=3D'mso-spacerun:yes'>    </span>is the number of time= s coin m is </span></span><span style=3D'position:absolute;top:56.5%;left:20.78%; width:75.65%;height:6.5%'><span lang=3DEN-US style=3D'font-family:Verdana; mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana;font-size:97%'= >sampled. </span></span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-margin-left-alt:348; direction:ltr;position:absolute;top:63.75%;left:14.79%;width:81.64%; height:6.5%'><span style=3D'mso-special-format:nobullet;display:none;color= :#006666; mso-color-index:3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:97%;display:none'> </span></di= v> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-margin-left-alt:348; direction:ltr'><span style=3D'position:absolute;top:71.25%;left:14.79%; width:89.13%;height:6.5%'><span style=3D'mso-special-format:nobullet;displ= ay: none;color:#006666;mso-color-index:3;font-family:Wingdings;font-size:70%'>= ¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:97%'><span style=3D'mso-spacerun:yes'>     </span>is the total nu= mber of heads when </span></span><span style=3D'position:absolute;top:77.5%; left:20.78%;width:75.65%;height:6.5%'><span lang=3DEN-US style=3D'font-fam= ily: Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana; font-size:97%'>sampling coin </span><span lang=3DEN-US style=3D'font-famil= y:Verdana; mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana;font-size:97%'= ><i>m</i></span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:97%'> for </span><span lang=3DEN-US 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style=3D'margin:0px;background-color:black' onclick=3D"DocumentOnClick()" onresize=3D"_RSW()" onload=3D"LoadSld()" onkeypress=3D"_KPH()"> <div id=3DSlideObj class=3Dsld style=3D'position:absolute;top:0px;left:0px; width:534px;height:400px;font-size:16px;background-color:white;clip:rect(0%= , 101%, 101%, 0%); visibility:hidden'><p:slide coordsize=3D"720,540" colors=3D"#FFFFFF,#000000,#5F5F5F,#006666,#33CCCC,#99CCCC,#006666,#B2B2B2" masterhref=3D"master06.xml"> <p:shaperange href=3D"master06.xml#_x0000_s6145"/><![if !ppt]><p:shaperange href=3D"master06.xml#_x0000_s6146"/><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s6146,_x0000_s6147,_x0000_s6148,_x0000_s6149" src=3D"master06_image002.gif" style=3D'position:absolute;top:4.0%;left:0%; width:95.5%;height:48.0%'><![endif]><p:shaperange href=3D"master06.xml#_x0000_s6153"/> <div dir=3DLTR v:shape=3D"_x0000_s6153" class=3DO style=3D'text-align:cent= er; direction:ltr;position:absolute;top:94.5%;left:35.2%;width:29.77%;height:3= .0%'><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:67%;mso-field-code:meta15'>COLT 2003</span><span style=3D'font-f= amily: Verdana;mso-ascii-font-family:Verdana;font-size:67%;mso-special-format:las= tCR; display:none'> </span></div> <p:shaperange href=3D"master06.xml#_x0000_s6154"/> <div v:shape=3D"_x0000_s6154" class=3DO> <div dir=3DLTR style=3D'direction:ltr;position:absolute;top:94.5%;left:72.= 65%; width:21.53%;height:3.0%'><span lang=3DAR-SA style=3D'font-family:Arial; mso-ascii-font-family:Verdana;mso-bidi-font-family:Arial;font-size:67%; mso-field-code:meta16' dir=3Drtl><span dir=3Dltr></span>10</span><span style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:67%; mso-special-format:lastCR;display:none'> </span></div> </div> <![endif]><p:shaperange href=3D"master06.xml#_x0000_m6150"/><v:shape id=3D= "_x0000_s123908" type=3D"#_x0000_m6150" style=3D'position:absolute;left:107.875pt;top:23.7= 5pt; width:575.875pt;height:90pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"title"/></v:shape><p:shaperange href=3D"master06.xml#_x0000_m6151"/><v:shape id=3D"_x0000_s123909" type= =3D"#_x0000_m6151" style=3D'position:absolute;left:107.875pt;top:143.875pt;width:281.875pt; height:324pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"body" position=3D"1" size=3D"half"/></v:shape> <div dir=3DRTL v:shape=3D"_x0000_s123908" class=3DT style=3D'position:abso= lute; top:12.75%;left:15.91%;width:78.08%;height:7.75%'><span lang=3DEN-US dir= =3Dltr>Proof (cont’)</span></div> <div v:shape=3D"_x0000_s123909" class=3DHB> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"95 20 35";direct= ion: ltr;position:absolute;top:27.0%;left:15.91%;width:43.82%;height:5.75%'><sp= an style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana'>Consider the events: </span></div> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:35.25%;left:15.91%;width:37.26%;height:5.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana'>1.<span style=3D'mso-spacerun:yes'>  </span> </span></div> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:41.25%;left:15.91%;width:37.26%;height:5.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;display:none'>&= #13;</span></div> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:47.25%;left:15.91%;width:37.26%;height:5.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana'>2.<span style=3D'mso-spacerun:yes'>     </span> </span></d= iv> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:53.5%;left:15.91%;width:37.26%;height:5.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;display:none'>&= #13;</span></div> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:59.5%;left:15.91%;width:37.26%;height:5.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana'>3. </span>= </div> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:65.75%;left:15.91%;width:37.26%;height:5.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;display:none'>&= #13;</span></div> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:71.75%;left:15.91%;width:37.26%;height:5.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 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xmlns:v=3D"urn:schemas-microsoft-com:vml" xmlns:o=3D"urn:schemas-microsoft-com:office:office" xmlns:p=3D"urn:schemas-microsoft-com:office:powerpoint" xmlns:oa=3D"urn:schemas-microsoft-com:office:activation" xmlns=3D"http://www.w3.org/TR/REC-html40"> <head> <meta http-equiv=3DContent-Type content=3D"text/html; charset=3Dus-ascii"> <meta name=3DProgId content=3DPowerPoint.Slide> <meta name=3DGenerator content=3D"Microsoft PowerPoint 10"> <link id=3DMain-File rel=3DMain-File href=3D"../COLTMABtalk.htm"> <link rel=3DPreview href=3Dpreview.wmf> <link rel=3DOLE-Object-Data href=3Doledata.mso> <!--[if !mso]> <style> v\:* {behavior:url(#default#VML);} o\:* {behavior:url(#default#VML);} p\:* {behavior:url(#default#VML);} .shape {behavior:url(#default#VML);} v\:textbox {display:none;} </style> <![endif]--> <title>Learning and Adaptation in Competitive and Dynamic Environment</titl= e> <![if IE]> <base href=3D"file:///C:\C65B91EB\COLTMABtalk_files\slide0007.htm" id=3D"webarch_temp_base_tag"> <![endif]> <meta name=3DDescription content=3D"8/28/2003: Proof (cont’)"> <link rel=3DStylesheet href=3D"master06_stylesheet.css"> <![if !ppt]> <style media=3Dprint> <!--.sld {left:0px !important; width:6.0in !important; height:4.5in !important; font-size:107% !important;} --> </style> <script src=3Dscript.js></script><script><!-- if( !IsNts() ) Redirect( "PPTSld" ); //--></script><!--[if vml]><script>g_vml =3D 1; </script><![endif]--><![endif]><p:slidetransition advancetime=3D"84112" flag=3D"1025"/><o:shapelayout v:ext=3D"edit"> <o:idmap v:ext=3D"edit" data=3D"14"/> </o:shapelayout> </head> <body lang=3DEN-US style=3D'margin:0px;background-color:black' onclick=3D"DocumentOnClick()" onresize=3D"_RSW()" onload=3D"LoadSld()" onkeypress=3D"_KPH()"> <div id=3DSlideObj class=3Dsld style=3D'position:absolute;top:0px;left:0px; width:534px;height:400px;font-size:16px;background-color:white;clip:rect(0%= , 101%, 101%, 0%); visibility:hidden'><p:slide coordsize=3D"720,540" colors=3D"#FFFFFF,#000000,#5F5F5F,#006666,#33CCCC,#99CCCC,#006666,#B2B2B2" masterhref=3D"master06.xml"> <p:shaperange href=3D"master06.xml#_x0000_s6145"/><![if !ppt]><p:shaperange href=3D"master06.xml#_x0000_s6146"/><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s6146,_x0000_s6147,_x0000_s6148,_x0000_s6149" src=3D"master06_image002.gif" style=3D'position:absolute;top:4.0%;left:0%; width:95.5%;height:48.0%'><![endif]><p:shaperange href=3D"master06.xml#_x0000_s6153"/> <div dir=3DLTR v:shape=3D"_x0000_s6153" class=3DO style=3D'text-align:cent= er; direction:ltr;position:absolute;top:94.5%;left:35.2%;width:29.77%;height:3= .0%'><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:67%;mso-field-code:meta15'>COLT 2003</span><span style=3D'font-f= amily: Verdana;mso-ascii-font-family:Verdana;font-size:67%;mso-special-format:las= tCR; display:none'> </span></div> <p:shaperange href=3D"master06.xml#_x0000_s6154"/> <div v:shape=3D"_x0000_s6154" class=3DO> <div dir=3DLTR style=3D'direction:ltr;position:absolute;top:94.5%;left:72.= 65%; width:21.53%;height:3.0%'><span lang=3DAR-SA style=3D'font-family:Arial; mso-ascii-font-family:Verdana;mso-bidi-font-family:Arial;font-size:67%; mso-field-code:meta16' dir=3Drtl><span dir=3Dltr></span>11</span><span style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:67%; mso-special-format:lastCR;display:none'> </span></div> </div> <![endif]><p:shaperange href=3D"master06.xml#_x0000_m6150"/><v:shape id=3D= "_x0000_s14338" type=3D"#_x0000_m6150" style=3D'position:absolute;left:107.875pt;top:23.7= 5pt; width:575.875pt;height:90pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"title"/></v:shape><p:shaperange href=3D"master06.xml#_x0000_m6151"/><v:shape id=3D"_x0000_s14339" type=3D= "#_x0000_m6151" style=3D'position:absolute;left:107.875pt;top:143.875pt;width:592.375pt; height:358.625pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"body" position=3D"1" size=3D"half"/></v:shape> <div dir=3DLTR v:shape=3D"_x0000_s14338" class=3DT style=3D'direction:ltr;= position: absolute;top:12.75%;left:15.91%;width:78.08%;height:7.75%'><span lang=3DEN= -US>Proof (cont’)</span></div> <div v:shape=3D"_x0000_s14339" class=3DHB> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:26.75%;left:15.91%;width:91.19%;height:5.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:96%'>= Lemma:<span style=3D'mso-spacerun:yes'>        = ;            &n= bsp;            = ;       </span>(<span style=3D'mso-spacerun:yes'>        = ;  </span>) </span></div> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:32.75%;left:15.91%;width:80.52%;height:5.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:96%; display:none'> </span></div> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:38.5%;left:15.91%;width:80.52%;height:5.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:96%'>= For small </span><span lang=3DEL style=3D'font-family:Arial;mso-ascii-font-fam= ily: Verdana;mso-bidi-font-family:Arial;mso-hansi-font-family:Verdana;font-size: 96%'>δ</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-asci= i-font-family: Verdana;mso-hansi-font-family:Verdana;font-size:96%;display:none'> </s= pan></div> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:44.5%;left:15.91%;width:80.52%;height:5.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:96%;display:none'> </span></div> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:50.25%;left:15.91%;width:80.52%;height:5.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:96%;display:none'> </span></div> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:56.0%;left:15.91%;width:80.52%;height:5.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:96%;display:none'> </span></div> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:62.0%;left:15.91%;width:80.52%;height:5.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:96%'>Lemma: </span></div> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:67.75%;left:15.91%;width:80.52%;height:5.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:96%;display:none'> </span></div> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:73.75%;left:15.91%;width:93.82%;height:5.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:96%'>“Amount of time spent sampling </span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:96%'><i>m</i></span><span lang=3DE= N-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:96%'> under </span><span lang=3DEN-US style=3D'font-fami= ly:Verdana; mso-ascii-font-family:Verdana'><i>H</i></span><span lang=3DEN-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-bidi-font-fam= ily: Arial;mso-hansi-font-family:Verdana;font-size:67%;position:relative; top:.37em;mso-text-raise:-25%'><i>ℓ</i></span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:96%'><span style=3D'mso-spacerun:yes'> </span>is &#= 13;</span></div> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:79.75%;left:15.91%;width:92.13%;height:5.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:96%'><span style=3D'mso-spacerun:yes'>  </span>small implies probability of choosing </span><span lang=3DEN-US style=3D'font-fa= mily: Arial;mso-ascii-font-family:Verdana;mso-bidi-font-family:Arial;mso-hansi-f= ont-family: Verdana;font-size:96%'><i>ℓ</i></span><span lang=3DEN-US style=3D'fo= nt-family: Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana; font-size:96%'> under </span></div> <div dir=3DLTR style=3D'text-align:left;mso-line-spacing:"90 20 0";directi= on:ltr; position:absolute;top:85.75%;left:15.91%;width:80.52%;height:5.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#006666;mso-color-= index: 3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana'><i><span style=3D'mso-spacerun:yes'>  </span>H</i></span><span lang=3DEN-US 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mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana;font-size:97%'= >define</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; display:none'> </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:49.75%;left:15.91%;width:78.08%;height:6.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;display:none'> </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:57.5%;left:15.91%;width:78.08%;height:6.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;display:none'> </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:65.25%;left:15.91%;width:78.08%;height:6.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana'>When </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:73.0%;left:15.91%;width:78.08%;height:6.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;display:none'> </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:80.75%;left:15.91%;width:78.08%;height:6.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US 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<head> <meta http-equiv=3DContent-Type content=3D"text/html; charset=3Dus-ascii"> <meta name=3DProgId content=3DPowerPoint.Slide> <meta name=3DGenerator content=3D"Microsoft PowerPoint 10"> <link id=3DMain-File rel=3DMain-File href=3D"../COLTMABtalk.htm"> <link rel=3DPreview href=3Dpreview.wmf> <link rel=3DOLE-Object-Data href=3Doledata.mso> <!--[if !mso]> <style> v\:* {behavior:url(#default#VML);} o\:* {behavior:url(#default#VML);} p\:* {behavior:url(#default#VML);} .shape {behavior:url(#default#VML);} v\:textbox {display:none;} </style> <![endif]--> <title>Learning and Adaptation in Competitive and Dynamic Environment</titl= e> <![if IE]> <base href=3D"file:///C:\C65B91EB\COLTMABtalk_files\slide0048.htm" id=3D"webarch_temp_base_tag"> <![endif]> <meta name=3DDescription content=3D"8/28/2003: Proof (cont’)"> <link rel=3DStylesheet href=3D"master06_stylesheet.css"> <![if !ppt]> <style media=3Dprint> <!--.sld {left:0px !important; width:6.0in !important; height:4.5in !important; 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dir=3Drtl><span dir=3Dltr></span>13</span><span style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:67%; mso-special-format:lastCR;display:none'> </span></div> </div> <![endif]><p:shaperange href=3D"master06.xml#_x0000_m6150"/><v:shape id=3D= "_x0000_s135170" type=3D"#_x0000_m6150" style=3D'position:absolute;left:107.875pt;top:23.7= 5pt; width:575.875pt;height:90pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"title"/></v:shape><p:shaperange href=3D"master06.xml#_x0000_m6151"/><v:shape id=3D"_x0000_s135171" type= =3D"#_x0000_m6151" style=3D'position:absolute;left:107.875pt;top:143.875pt;width:575.875pt; height:381.25pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"body" position=3D"1"/></v:shape> <div dir=3DRTL v:shape=3D"_x0000_s135170" class=3DT style=3D'position:abso= lute; top:12.75%;left:15.91%;width:78.08%;height:7.75%'><span lang=3DEN-US dir= =3Dltr>Proof (cont’)</span></div> <div v:shape=3D"_x0000_s135171"> <div class=3DB1 style=3D'mso-margin-left-alt:588'></div> <div class=3DB2 style=3D'mso-margin-left-alt:840'></div> <div class=3DB3 style=3D'mso-margin-left-alt:1092'></div> <div class=3DB4 style=3D'mso-margin-left-alt:1380'></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-line-spacing:"80 20 = 0"; mso-margin-left-alt:348;direction:ltr;position:absolute;top:26.25%;left:15= .91%; width:78.08%;height:5.75%'><span style=3D'mso-special-format:nobullet; display:none;color:#006666;mso-color-index:3;font-family:Wingdings;font-si= ze: 70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-asc= ii-font-family: Verdana;mso-hansi-font-family:Verdana;font-size:86%'>When<span style=3D'mso-spacerun:yes'>       </span>hol= ds, under </span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-fon= t-family: Verdana;mso-hansi-font-family:Verdana;font-size:86%'><i>H</i></span><span lang=3DEN-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-= bidi-font-family: Arial;mso-hansi-font-family:Verdana;font-size:57%;position:relative; top:.37em;mso-text-raise:-25%'><i>ℓ</i></span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:57%;position:relative;top:.37em;mso-text-raise:-25%'><i>= <span style=3D'mso-spacerun:yes'> </span></i></span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:86%'>: </span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-line-spacing:"80 20 = 0"; mso-margin-left-alt:348;direction:ltr;position:absolute;top:32.0%;left:15.= 91%; width:78.08%;height:5.75%'><span style=3D'mso-special-format:nobullet; display:none;color:#006666;mso-color-index:3;font-family:Wingdings;font-si= ze: 70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-asc= ii-font-family: Verdana;mso-hansi-font-family:Verdana;font-size:86%;display:none'> </s= pan></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-line-spacing:"80 20 = 0"; mso-margin-left-alt:348;direction:ltr'><span style=3D'position:absolute; top:37.5%;left:22.09%;width:82.39%;height:5.75%'><span style=3D'font-size:= 86%'><span style=3D'mso-special-format:"numbullet3\,1";color:#006666;mso-color-index:= 3; position:absolute;left:-7.5%;top:.39em;font-size:70%'>1.</span></span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:86%'>For each sample path the coins behave </span></span><span style=3D'position:absolute;top:42.0%;left:22.09= %; width:72.09%;height:5.75%'><span lang=3DEN-US style=3D'font-family:Verdana; mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana;font-size:86%'= >as predicted by their p's. </span></span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-line-spacing:"80 20 = 0"; mso-margin-left-alt:348;direction:ltr'><span style=3D'position:absolute; top:47.5%;left:22.09%;width:81.27%;height:5.75%'><span style=3D'font-size:= 86%'><span style=3D'mso-special-format:"numbullet3\,1";color:#006666;mso-color-index:= 3; position:absolute;left:-7.6%;top:.39em;font-size:70%'>2.</span></span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:86%'>Correctness implies that for = most such </span></span><span style=3D'position:absolute;top:52.0%;left:22.09%; width:72.09%;height:5.75%'><span lang=3DEN-US style=3D'font-family:Verdana; mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana;font-size:86%'= >paths hypothesis </span><span lang=3DEN-US style=3D'font-family:Verdana;mso-asci= i-font-family: Verdana;mso-hansi-font-family:Verdana;font-size:86%'><i>H</i></span><span lang=3DEN-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-= bidi-font-family: Arial;mso-hansi-font-family:Verdana;font-size:57%;position:relative; top:.37em;mso-text-raise:-25%'><i>ℓ</i></span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:86%'><span style=3D'mso-spacerun:yes'> </span>is chosen.<br> </span></span><span style=3D'position:absolute;top:56.25%;left:22.09%; width:72.09%;height:5.75%'><span lang=3DEN-US style=3D'font-family:Verdana; mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana;font-size:86%'= ><br> </span></span><span style=3D'position:absolute;top:60.75%;left:22.09%; width:72.09%;height:5.75%'><span lang=3DEN-US style=3D'font-family:Verdana; mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana;font-size:86%; display:none'> </span></span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-line-spacing:"80 20 = 0"; mso-margin-left-alt:348;direction:ltr;position:absolute;top:66.25%;left:15= .91%; width:78.08%;height:5.75%'><span style=3D'mso-special-format:nobullet; display:none;color:#006666;mso-color-index:3;font-family:Wingdings;font-si= ze: 70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-asc= ii-font-family: Verdana;mso-hansi-font-family:Verdana;font-size:86%'>Under hypothesis </sp= an><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:86%'><i>H</i></span><span lang=3DE= N-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:57%;position:relative;top:.37em;mso-text-raise:-25%'><i>= m</i></span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:86%'><span style=3D'mso-spacerun:yes'> </span>: </span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-line-spacing:"80 20 = 0"; mso-margin-left-alt:348;direction:ltr'><span style=3D'position:absolute; top:72.0%;left:22.09%;width:81.64%;height:5.75%'><span style=3D'font-size:= 86%'><span style=3D'mso-special-format:"numbullet3\,1";color:#006666;mso-color-index:= 3; position:absolute;left:-7.56%;top:.39em;font-size:70%'>1.</span></span><sp= an lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:86%'>Such paths have </span><span lang=3DEL style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-bid= i-font-family: Arial;mso-hansi-font-family:Verdana;font-size:83%'>δ</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:83%'> </span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:86%'><span style=3D'mso-spacerun:yes'> </span>proba= bility (proved </span></span><span style=3D'position:absolute;top:76.25%;left:22.= 09%; width:72.09%;height:5.75%'><span lang=3DEN-US style=3D'font-family:Verdana; mso-ascii-font-family:Verdana;mso-hansi-font-family:Verdana;font-size:86%'= >by bounding likelihood ratio). </span></span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-line-spacing:"80 20 = 0"; mso-margin-left-alt:348;direction:ltr;position:absolute;top:82.0%;left:15.= 91%; width:78.08%;height:5.75%'><span style=3D'position:absolute;top:0%;left:7.= 91%; width:92.32%;height:100.0%'><span style=3D'font-size:86%;font-style:italic= '><span style=3D'mso-special-format:"numbullet3\,1";color:#006666;mso-color-index:= 3; position:absolute;left:-8.57%;top:.39em;font-size:70%'>2.</span></span><sp= an lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:86%'><i>H</i></span><span lang=3DE= N-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-bidi-font-fam= ily: Arial;mso-hansi-font-family:Verdana;font-size:57%;position:relative; top:.37em;mso-text-raise:-25%'><i>ℓ</i></span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:86%'><span style=3D'mso-spacerun:yes'> </span>is ag= ain selected. </span></span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-line-spacing:"80 20 = 0"; mso-margin-left-alt:348;direction:ltr;position:absolute;top:87.5%;left:15.= 91%; width:92.5%;height:5.75%'><span style=3D'mso-special-format:nobullet;displ= ay: none;color:#006666;mso-color-index:3;font-family:Wingdings;font-size:70%'>= ¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:86%'><span style=3D'mso-tab-count:= 1; width:6.53%'> </span><span style=3D'mso-spacerun:yes'>   </span>= <span style=3D'mso-tab-count:7;width:65.19%'> </span><span style=3D'mso-spacerun:yes'>    </span></span><span lang=3DEN-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-= bidi-font-family: Arial;mso-hansi-font-family:Verdana;font-size:86%'>□</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:86%;mso-special-format:lastCR; display:none'> </span></div> </div> <v:shapetype id=3D"_x0000_t75" coordsize=3D"21600,21600" o:spt=3D"75" o:preferrelative=3D"t" path=3D"m@4@5l@4@11@9@11@9@5xe" filled=3D"f" strok= ed=3D"f"> <v:stroke joinstyle=3D"miter"/> <v:formulas> <v:f eqn=3D"if lineDrawn pixelLineWidth 0"/> <v:f eqn=3D"sum @0 1 0"/> <v:f eqn=3D"sum 0 0 @1"/> <v:f eqn=3D"prod @2 1 2"/> <v:f eqn=3D"prod @3 21600 pixelWidth"/> <v:f eqn=3D"prod @3 21600 pixelHeight"/> <v:f eqn=3D"sum @0 0 1"/> <v:f eqn=3D"prod @6 1 2"/> <v:f eqn=3D"prod @7 21600 pixelWidth"/> <v:f eqn=3D"sum @8 21600 0"/> <v:f eqn=3D"prod @7 21600 pixelHeight"/> <v:f eqn=3D"sum @10 21600 0"/> </v:formulas> <v:path o:extrusionok=3D"f" gradientshapeok=3D"t" o:connecttype=3D"rect"/> <o:lock v:ext=3D"edit" aspectratio=3D"t"/> </v:shapetype><v:shape 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href=3D"master06.xml#_x0000_s6145"/><![if !ppt]><p:shaperange href=3D"master06.xml#_x0000_s6146"/><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s6146,_x0000_s6147,_x0000_s6148,_x0000_s6149" src=3D"master06_image002.gif" style=3D'position:absolute;top:4.0%;left:0%; width:95.5%;height:48.0%'><![endif]><p:shaperange href=3D"master06.xml#_x0000_s6153"/> <div dir=3DLTR v:shape=3D"_x0000_s6153" class=3DO style=3D'text-align:cent= er; direction:ltr;position:absolute;top:94.5%;left:35.2%;width:29.77%;height:3= .0%'><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:67%;mso-field-code:meta15'>COLT 2003</span><span style=3D'font-f= amily: Verdana;mso-ascii-font-family:Verdana;font-size:67%;mso-special-format:las= tCR; display:none'> </span></div> <p:shaperange href=3D"master06.xml#_x0000_s6154"/> <div v:shape=3D"_x0000_s6154" class=3DO> <div dir=3DLTR style=3D'direction:ltr;position:absolute;top:94.5%;left:72.= 65%; width:21.53%;height:3.0%'><span lang=3DAR-SA style=3D'font-family:Arial; mso-ascii-font-family:Verdana;mso-bidi-font-family:Arial;font-size:67%; mso-field-code:meta16' dir=3Drtl><span dir=3Dltr></span>14</span><span style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:67%; mso-special-format:lastCR;display:none'> </span></div> </div> <![endif]><p:shaperange href=3D"master06.xml#_x0000_m6150"/><v:shape id=3D= "_x0000_s128002" type=3D"#_x0000_m6150" style=3D'position:absolute;left:107.875pt;top:23.7= 5pt; width:575.875pt;height:90pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"title"/></v:shape><p:shaperange href=3D"master06.xml#_x0000_m6151"/><v:shape id=3D"_x0000_s128003" type= =3D"#_x0000_m6151" style=3D'position:absolute;left:107.875pt;top:143.875pt;width:575.875pt; height:324pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"body" position=3D"1"/></v:shape> <div dir=3DRTL v:shape=3D"_x0000_s128002" class=3DT style=3D'position:abso= lute; top:12.75%;left:15.91%;width:78.08%;height:7.75%'><span lang=3DEN-US dir= =3Dltr>Proof (cont’)</span></div> <div v:shape=3D"_x0000_s128003" class=3DB> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:27.25%;left:15.91%;width:80.89%;height:6.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana'>Since the policy is </span><span lang=3DEL style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-bidi-font-fam= ily: Arial;mso-hansi-font-family:Verdana;font-size:97%'>ε</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; mso-hansi-font-family:Verdana;font-size:97%'>-</span><span lang=3DEN-US style=3D'font-family:Symbol;mso-ascii-font-family:Verdana;mso-hansi-font-f= amily: Verdana;font-size:97%;mso-char-type:symbol'>d</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:97%'> correct</span><span lang=3DEN-US style=3D'font-fam= ily: Verdana;mso-ascii-font-family:Verdana'> and </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:35.0%;left:15.91%;width:78.08%;height:6.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;display:none'> </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:42.75%;left:15.91%;width:78.08%;height:6.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;display:none'> </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:50.5%;left:15.91%;width:78.08%;height:6.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana'>We have that<span style=3D'mso-spacerun:yes'>        = ;        </span>for all </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:58.25%;left:15.91%;width:78.08%;height:6.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;display:none'> </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:66.0%;left:15.91%;width:78.08%;height:6.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana'>Result follows by summing over </span>= </div> <div dir=3DRTL style=3D'position:absolute;top:74.0%;left:15.91%;width:78.0= 8%; height:6.25%'><span style=3D'mso-special-format:nobullet;display:none; color:#006666;mso-color-index:3;font-family:Wingdings;font-size:70%'>&iexc= l;</span><span lang=3DEN-US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-= bidi-font-family: Arial;mso-hansi-font-family:Verdana' dir=3Dltr>□</span><span lang=3D= EN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;mso-hansi-font-= family: Verdana;font-size:66%;mso-text-raise:-25%;mso-special-format:lastCR; display:none' dir=3Drtl><sub> </sub></span></div> </div> 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v:shapes=3D"_x0000_s6146,_x0000_s6147,_x0000_s6148,_x0000_s6149" src=3D"master06_image002.gif" style=3D'position:absolute;top:4.0%;left:0%; width:95.5%;height:48.0%'><![endif]><p:shaperange href=3D"master06.xml#_x0000_s6153"/> <div dir=3DLTR v:shape=3D"_x0000_s6153" class=3DO style=3D'text-align:cent= er; direction:ltr;position:absolute;top:94.5%;left:35.2%;width:29.77%;height:3= .0%'><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:67%;mso-field-code:meta15'>COLT 2003</span><span style=3D'font-f= amily: Verdana;mso-ascii-font-family:Verdana;font-size:67%;mso-special-format:las= tCR; display:none'> </span></div> <p:shaperange href=3D"master06.xml#_x0000_s6154"/> <div v:shape=3D"_x0000_s6154" class=3DO> <div dir=3DLTR style=3D'direction:ltr;position:absolute;top:94.5%;left:72.= 65%; width:21.53%;height:3.0%'><span lang=3DAR-SA style=3D'font-family:Arial; mso-ascii-font-family:Verdana;mso-bidi-font-family:Arial;font-size:67%; mso-field-code:meta16' dir=3Drtl><span dir=3Dltr></span>15</span><span style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:67%; mso-special-format:lastCR;display:none'> </span></div> </div> <![endif]><p:shaperange href=3D"master06.xml#_x0000_m6150"/><v:shape id=3D= "_x0000_s130050" type=3D"#_x0000_m6150" style=3D'position:absolute;left:107.875pt;top:23.7= 5pt; width:575.875pt;height:90pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"title"/></v:shape><p:shaperange href=3D"master06.xml#_x0000_m6151"/><v:shape id=3D"_x0000_s130051" type= =3D"#_x0000_m6151" style=3D'position:absolute;left:107.875pt;top:143.875pt;width:575.875pt; height:324pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"body" position=3D"1"/></v:shape> <div dir=3DRTL v:shape=3D"_x0000_s130050" class=3DT style=3D'position:abso= lute; top:12.75%;left:15.91%;width:78.08%;height:7.75%'><span lang=3DEN-US dir= =3Dltr>The Bayesian Setup</span></div> <div v:shape=3D"_x0000_s130051"> <div class=3DB1 style=3D'mso-margin-left-alt:588'></div> <div class=3DB2 style=3D'mso-margin-left-alt:840'></div> <div class=3DB3 style=3D'mso-margin-left-alt:1092'></div> <div class=3DB4 style=3D'mso-margin-left-alt:1380'></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-margin-left-alt:348; direction:ltr;position:absolute;top:27.25%;left:15.91%;width:78.08%; height:5.75%'><span style=3D'mso-special-format:nobullet;display:none; color:#006666;mso-color-index:3;font-family:Wingdings;font-size:70%'>&iexc= l;</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:86%'>A weaker notion of optimality: </span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-margin-left-alt:348; direction:ltr;position:absolute;top:34.0%;left:15.91%;width:78.08%;height: 6.0%'><span style=3D'mso-special-format:nobullet;display:none;color:#00666= 6; mso-color-index:3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:86%'>A strategy is </span><span lang=3DEL style=3D'font-family:A= rial; mso-ascii-font-family:Verdana;mso-bidi-font-family:Arial;font-size:86%'>&#= 949;</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:86%'>-</span><span lang=3DEN-US style=3D'font-family:Symbol;mso-= ascii-font-family: Verdana;font-size:86%;mso-char-type:symbol'>d</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:86%'> correct with respect </span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-margin-left-alt:348; direction:ltr;position:absolute;top:40.5%;left:15.91%;width:78.08%;height: 5.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#0066= 66; mso-color-index:3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:86%'>to a prior p (on the biases) if: </span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-margin-left-alt:348; direction:ltr;position:absolute;top:47.25%;left:15.91%;width:78.08%; height:5.75%'><span style=3D'position:absolute;top:0%;left:7.91%;width:92.= 32%; height:100.0%'><span style=3D'font-size:86%'><span style=3D'mso-special-fo= rmat: "numbullet3\,1";color:#006666;mso-color-index:3;position:absolute;left:-8.= 57%; top:.39em;font-size:70%'>1.</span></span><span lang=3DEN-US style=3D'font-= family: Verdana;mso-ascii-font-family:Verdana;font-size:86%'>It terminates w.p.1&#= 13;</span></span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-margin-left-alt:348; direction:ltr'><span style=3D'position:absolute;top:54.0%;left:22.09%; width:80.89%;height:6.0%'><span style=3D'font-size:86%'><span style=3D'mso= -special-format: "numbullet3\,1";color:#006666;mso-color-index:3;position:absolute;left:-7.= 63%; top:.39em;font-size:70%'>2.</span></span><span lang=3DEN-US style=3D'font-= family: Verdana;mso-ascii-font-family:Verdana;font-size:86%'>W.p. at least 1- </sp= an><span lang=3DEN-US style=3D'font-family:Symbol;mso-ascii-font-family:Verdana;fon= t-size: 86%;mso-char-type:symbol'>d</span><span lang=3DEN-US style=3D'font-family:= Verdana; mso-ascii-font-family:Verdana;font-size:86%'> (</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:86%; color:red'>w.r.t. the prior</span><span lang=3DEN-US style=3D'font-family:= Verdana; mso-ascii-font-family:Verdana;font-size:86%'>) the </span></span><span style=3D'position:absolute;top:59.5%;left:22.09%;width:83.7%;height:5.75%'= ><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:86%'>coin chosen is at most </span><span lang=3DEL style=3D'font= -family: Arial;mso-ascii-font-family:Verdana;mso-bidi-font-family:Arial;font-size:8= 6%'>ε</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:86%'>-worse than the </span></span><span style=3D'position:absol= ute; top:65.0%;left:22.09%;width:72.09%;height:5.75%'><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:86%'>= best coin. </span></span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-margin-left-alt:348; direction:ltr;position:absolute;top:71.75%;left:15.91%;width:78.08%; height:5.75%'><span style=3D'mso-special-format:nobullet;display:none; color:#006666;mso-color-index:3;font-family:Wingdings;font-size:70%'>&iexc= l;</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:86%;display:none'> </span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-margin-left-alt:348; direction:ltr;position:absolute;top:78.5%;left:15.91%;width:78.08%;height: 5.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#0066= 66; mso-color-index:3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:86%'>A similar result holds. </span></div> <div dir=3DLTR class=3DB style=3D'text-align:left;mso-margin-left-alt:348; direction:ltr;position:absolute;top:85.0%;left:15.91%;width:78.08%;height: 5.75%'><span style=3D'mso-special-format:nobullet;display:none;color:#0066= 66; mso-color-index:3;font-family:Wingdings;font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:86%;mso-special-format:lastCR;display:none'> </span></div> </div> </p:slide></div> </body> </html> ------=_NextPart_01C36D5C.68A97260 Content-Location: file:///C:/C65B91EB/COLTMABtalk_files/slide0044.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" <html xmlns:v=3D"urn:schemas-microsoft-com:vml" xmlns:o=3D"urn:schemas-microsoft-com:office:office" xmlns:p=3D"urn:schemas-microsoft-com:office:powerpoint" xmlns:oa=3D"urn:schemas-microsoft-com:office:activation" xmlns=3D"http://www.w3.org/TR/REC-html40"> <head> <meta http-equiv=3DContent-Type content=3D"text/html; charset=3Dus-ascii"> <meta name=3DProgId content=3DPowerPoint.Slide> <meta name=3DGenerator content=3D"Microsoft PowerPoint 10"> <link id=3DMain-File rel=3DMain-File href=3D"../COLTMABtalk.htm"> <link rel=3DPreview href=3Dpreview.wmf> <link rel=3DOLE-Object-Data href=3Doledata.mso> <!--[if !mso]> <style> v\:* {behavior:url(#default#VML);} o\:* {behavior:url(#default#VML);} p\:* {behavior:url(#default#VML);} .shape {behavior:url(#default#VML);} v\:textbox {display:none;} </style> <![endif]--> <title>Learning and Adaptation in Competitive and Dynamic Environment</titl= e> <![if IE]> <base href=3D"file:///C:\C65B91EB\COLTMABtalk_files\slide0044.htm" id=3D"webarch_temp_base_tag"> <![endif]> <meta name=3DDescription content=3D"8/28/2003: The case of given biases"> <link rel=3DStylesheet href=3D"master06_stylesheet.css"> <![if !ppt]> <style media=3Dprint> <!--.sld {left:0px !important; width:6.0in !important; height:4.5in !important; font-size:107% !important;} --> </style> <script src=3Dscript.js></script><script><!-- if( !IsNts() ) Redirect( "PPTSld" ); //--></script><!--[if vml]><script>g_vml =3D 1; </script><![endif]--><![endif]><p:slidetransition advancetime=3D"116160" flag=3D"1025"/><o:shapelayout v:ext=3D"edit"> <o:idmap v:ext=3D"edit" data=3D"128"/> </o:shapelayout> </head> <body lang=3DEN-US style=3D'margin:0px;background-color:black' onclick=3D"DocumentOnClick()" onresize=3D"_RSW()" onload=3D"LoadSld()" onkeypress=3D"_KPH()"> <div id=3DSlideObj class=3Dsld style=3D'position:absolute;top:0px;left:0px; width:534px;height:400px;font-size:16px;background-color:white;clip:rect(0%= , 101%, 101%, 0%); visibility:hidden'><p:slide coordsize=3D"720,540" colors=3D"#FFFFFF,#000000,#5F5F5F,#006666,#33CCCC,#99CCCC,#006666,#B2B2B2" masterhref=3D"master06.xml"> <p:shaperange href=3D"master06.xml#_x0000_s6145"/><![if !ppt]><p:shaperange href=3D"master06.xml#_x0000_s6146"/><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s6146,_x0000_s6147,_x0000_s6148,_x0000_s6149" src=3D"master06_image002.gif" style=3D'position:absolute;top:4.0%;left:0%; width:95.5%;height:48.0%'><![endif]><p:shaperange href=3D"master06.xml#_x0000_s6153"/> <div dir=3DLTR v:shape=3D"_x0000_s6153" class=3DO style=3D'text-align:cent= er; direction:ltr;position:absolute;top:94.5%;left:35.2%;width:29.77%;height:3= .0%'><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:67%;mso-field-code:meta15'>COLT 2003</span><span style=3D'font-f= amily: Verdana;mso-ascii-font-family:Verdana;font-size:67%;mso-special-format:las= tCR; display:none'> </span></div> <p:shaperange href=3D"master06.xml#_x0000_s6154"/> <div v:shape=3D"_x0000_s6154" class=3DO> <div dir=3DLTR style=3D'direction:ltr;position:absolute;top:94.5%;left:72.= 65%; width:21.53%;height:3.0%'><span lang=3DAR-SA style=3D'font-family:Arial; mso-ascii-font-family:Verdana;mso-bidi-font-family:Arial;font-size:67%; mso-field-code:meta16' dir=3Drtl><span dir=3Dltr></span>16</span><span style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:67%; mso-special-format:lastCR;display:none'> </span></div> </div> <![endif]><p:shaperange href=3D"master06.xml#_x0000_m6150"/><v:shape id=3D= "_x0000_s131074" type=3D"#_x0000_m6150" style=3D'position:absolute;left:107.875pt;top:23.7= 5pt; width:575.875pt;height:90pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"title"/></v:shape><p:shaperange href=3D"master06.xml#_x0000_m6151"/><v:shape id=3D"_x0000_s131075" type= =3D"#_x0000_m6151" style=3D'position:absolute;left:107.875pt;top:143.875pt;width:575.875pt; height:324pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"body" position=3D"1"/></v:shape> <div dir=3DRTL v:shape=3D"_x0000_s131074" class=3DT style=3D'position:abso= lute; top:12.75%;left:15.91%;width:78.08%;height:7.75%'><span lang=3DEN-US dir= =3Dltr>The case of given biases</span></div> <div v:shape=3D"_x0000_s131075" class=3DB> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:27.25%;left:15.91%;width:78.08%;height:6.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana'>Suppose we want to bound the </span></= div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:35.0%;left:15.91%;width:83.14%;height:6.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana'>exploration time for a given set of </= span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:42.75%;left:15.91%;width:87.82%;height:6.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana'>biases, but unknown to the decision </= span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:50.5%;left:15.91%;width:78.08%;height:6.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana'>maker (</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana'><i>p*</i></spa= n><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana'> = is the best coin). </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:58.25%;left:15.91%;width:93.63%;height:6.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana'>Then every </span><span lang=3DEL style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-bidi-font-fam= ily: Arial'>ε</span><span lang=3DEN-US style=3D'font-family:Verdana;mso-as= cii-font-family: Verdana'>-</span><span lang=3DEN-US style=3D'font-family:Symbol;mso-ascii-= font-family: Verdana;mso-char-type:symbol'>d</span><span lang=3DEN-US style=3D'font-fam= ily: Verdana;mso-ascii-font-family:Verdana'> correct policy satisfies: </sp= an></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:66.0%;left:15.91%;width:78.08%;height:6.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;display:none'> </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:73.75%;left:15.91%;width:78.08%;height:6.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;display:none'> </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:81.25%;left:15.91%;width:78.08%;height:6.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; 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<meta name=3DGenerator content=3D"Microsoft PowerPoint 10"> <link id=3DMain-File rel=3DMain-File href=3D"../COLTMABtalk.htm"> <link rel=3DPreview href=3Dpreview.wmf> <link rel=3DOLE-Object-Data href=3Doledata.mso> <!--[if !mso]> <style> v\:* {behavior:url(#default#VML);} o\:* {behavior:url(#default#VML);} p\:* {behavior:url(#default#VML);} .shape {behavior:url(#default#VML);} v\:textbox {display:none;} </style> <![endif]--> <title>Learning and Adaptation in Competitive and Dynamic Environment</titl= e> <![if IE]> <base href=3D"file:///C:\C65B91EB\COLTMABtalk_files\slide0046.htm" id=3D"webarch_temp_base_tag"> <![endif]> <meta name=3DDescription content=3D"8/28/2003: Conclusions"> <link rel=3DStylesheet href=3D"master06_stylesheet.css"> <![if !ppt]> <style media=3Dprint> <!--.sld {left:0px !important; width:6.0in !important; height:4.5in !important; font-size:107% !important;} --> </style> <script src=3Dscript.js></script><script><!-- if( !IsNts() ) Redirect( "PPTSld" ); //--></script><!--[if vml]><script>g_vml =3D 1; </script><![endif]--><![endif]><p:slidetransition advancetime=3D"62544" flag=3D"1025"/><o:shapelayout v:ext=3D"edit"> <o:idmap v:ext=3D"edit" data=3D"130"/> </o:shapelayout> </head> <body lang=3DEN-US style=3D'margin:0px;background-color:black' onclick=3D"DocumentOnClick()" onresize=3D"_RSW()" onload=3D"LoadSld()" onkeypress=3D"_KPH()"> <div id=3DSlideObj class=3Dsld style=3D'position:absolute;top:0px;left:0px; width:534px;height:400px;font-size:16px;background-color:white;clip:rect(0%= , 101%, 101%, 0%); visibility:hidden'><p:slide coordsize=3D"720,540" colors=3D"#FFFFFF,#000000,#5F5F5F,#006666,#33CCCC,#99CCCC,#006666,#B2B2B2" masterhref=3D"master06.xml"> <p:shaperange href=3D"master06.xml#_x0000_s6145"/><![if !ppt]><p:shaperange href=3D"master06.xml#_x0000_s6146"/><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s6146,_x0000_s6147,_x0000_s6148,_x0000_s6149" src=3D"master06_image002.gif" style=3D'position:absolute;top:4.0%;left:0%; width:95.5%;height:48.0%'><![endif]><p:shaperange href=3D"master06.xml#_x0000_s6153"/> <div dir=3DLTR v:shape=3D"_x0000_s6153" class=3DO style=3D'text-align:cent= er; direction:ltr;position:absolute;top:94.5%;left:35.2%;width:29.77%;height:3= .0%'><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana; font-size:67%;mso-field-code:meta15'>COLT 2003</span><span style=3D'font-f= amily: Verdana;mso-ascii-font-family:Verdana;font-size:67%;mso-special-format:las= tCR; display:none'> </span></div> <p:shaperange href=3D"master06.xml#_x0000_s6154"/> <div v:shape=3D"_x0000_s6154" class=3DO> <div dir=3DLTR style=3D'direction:ltr;position:absolute;top:94.5%;left:72.= 65%; width:21.53%;height:3.0%'><span lang=3DAR-SA style=3D'font-family:Arial; mso-ascii-font-family:Verdana;mso-bidi-font-family:Arial;font-size:67%; mso-field-code:meta16' dir=3Drtl><span dir=3Dltr></span>17</span><span style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:67%; mso-special-format:lastCR;display:none'> </span></div> </div> <![endif]><p:shaperange href=3D"master06.xml#_x0000_m6150"/><v:shape id=3D= "_x0000_s133122" type=3D"#_x0000_m6150" style=3D'position:absolute;left:107.875pt;top:23.7= 5pt; width:575.875pt;height:90pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"title"/></v:shape><p:shaperange href=3D"master06.xml#_x0000_m6151"/><v:shape id=3D"_x0000_s133123" type= =3D"#_x0000_m6151" style=3D'position:absolute;left:107.875pt;top:143.875pt;width:575.875pt; height:364.25pt' o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"body" position=3D"1"/></v:shape> <div dir=3DRTL v:shape=3D"_x0000_s133122" class=3DT style=3D'position:abso= lute; top:12.75%;left:15.91%;width:78.08%;height:7.75%'><span lang=3DEN-US dir= =3Dltr>Conclusions</span></div> <div v:shape=3D"_x0000_s133123" class=3DB> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:27.25%;left:15.91%;width:78.08%;height:5.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:86%'>The complexity is </span= ></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:34.0%;left:15.91%;width:78.08%;height:5.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:86%;display:none'> </span></di= v> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:40.5%;left:15.91%;width:89.51%;height:5.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:86%'>We don</span><span lang=3DEN-= US style=3D'font-family:Arial;mso-ascii-font-family:Verdana;mso-hansi-font-fa= mily: Arial;font-size:86%'>’</span><span lang=3DEN-US style=3D'font-family= :Verdana; mso-ascii-font-family:Verdana;font-size:86%'>t gain much by dynamic decisions. </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:47.25%;left:15.91%;width:78.08%;height:5.75%'><span style=3D'mso-speci= al-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:86%;display:none'> </span></di= v> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:54.0%;left:15.91%;width:78.08%;height:5.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:86%'>Bayesian/permutations setup.&= #13;</span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:60.5%;left:15.91%;width:78.08%;height:5.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:86%;display:none'> </span></di= v> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:67.25%;left:15.91%;width:88.2%;height:5.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:86%'>Results can be extended to ri= cher random </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:74.0%;left:15.91%;width:78.08%;height:5.75%'><span style=3D'mso-specia= l-format: nobullet;display:none;color:#006666;mso-color-index:3;font-family:Wingding= s; font-size:70%'>¡</span><span lang=3DEN-US style=3D'font-family:Verda= na; mso-ascii-font-family:Verdana;font-size:86%'>variables.</span></div> </div> <v:shapetype id=3D"_x0000_t75" coordsize=3D"21600,21600" o:spt=3D"75" o:preferrelative=3D"t" path=3D"m@4@5l@4@11@9@11@9@5xe" filled=3D"f" strok= ed=3D"f"> <v:stroke joinstyle=3D"miter"/> <v:formulas> <v:f eqn=3D"if lineDrawn pixelLineWidth 0"/> <v:f eqn=3D"sum @0 1 0"/> <v:f eqn=3D"sum 0 0 @1"/> <v:f eqn=3D"prod @2 1 2"/> <v:f eqn=3D"prod @3 21600 pixelWidth"/> <v:f eqn=3D"prod @3 21600 pixelHeight"/> <v:f eqn=3D"sum @0 0 1"/> <v:f eqn=3D"prod @6 1 2"/> <v:f eqn=3D"prod @7 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id=3D"= _x0000_s134148" style=3D'position:absolute;left:121.875pt;top:457.125pt;width:550.75pt; height:62.375pt' filled=3D"f" fillcolor=3D"#3cc [4]" stroked=3D"f" stroke= color=3D"black [1]"> <v:fill color2=3D"white [0]"/> <v:shadow color=3D"#5f5f5f [2]"/> </v:rect> <div dir=3DLTR v:shape=3D"_x0000_s134146" class=3DCT style=3D'direction:lt= r'><span style=3D'position:absolute;top:8.5%;left:16.85%;width:87.64%;height:8.5%'>= <span lang=3DEN-US>Lower Bounds on the Sample </span></span><span style=3D'posit= ion: absolute;top:17.5%;left:16.85%;width:94.0%;height:8.5%'><span lang=3DEN-US= >Complexity of Exploration in the </span></span><span style=3D'position:absolute;top:2= 6.25%; left:16.85%;width:83.52%;height:8.5%'><span lang=3DEN-US>Multi-Armed Bandit Problem</span></span></div> <div v:shape=3D"_x0000_s134147" class=3DCB> <div dir=3DLTR style=3D'text-align:center;direction:ltr;position:absolute; = top:43.25%;left:19.47%;width:74.71%;height:5.75%'><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:83%'>= Shie Mannor </span></div> <div dir=3DLTR style=3D'text-align:center;direction:ltr;position:absolute; top:49.75%;left:19.47%;width:74.71%;height:5.75%'><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:83%'>= John N. Tsitsiklis </span></div> <div dir=3DLTR style=3D'text-align:center;direction:ltr;position:absolute; top:56.0%;left:19.47%;width:74.71%;height:5.75%'><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:83%; display:none'> </span></div> <div dir=3DLTR style=3D'text-align:left;direction:ltr;position:absolute; top:62.25%;left:19.47%;width:87.07%;height:5.0%'><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:72%'>= Laboratory for Information and Decision Systems </span></div> <div dir=3DLTR style=3D'text-align:center;direction:ltr;position:absolute; top:68.0%;left:19.47%;width:74.71%;height:5.0%'><span lang=3DEN-US style=3D'font-family:Verdana;mso-ascii-font-family:Verdana;font-size:72%'>= Massachusetts Institute of Technology</span></div> </div> <div dir=3DLTR v:shape=3D"_x0000_s134148" class=3DCB style=3D'text-align:c= enter; mso-line-spacing:"80 20 0";direction:ltr;position:absolute;top:84.0%; left:17.97%;width:74.71%;height:8.25%'><span lang=3DEN-US style=3D'font-fa= mily: Verdana;mso-ascii-font-family:Verdana;font-size:124%'>Thank You</span></di= v> </p:slide></div> </body> </html> ------=_NextPart_01C36D5C.68A97260 Content-Location: file:///C:/C65B91EB/COLTMABtalk_files/master01.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" <html xmlns:v=3D"urn:schemas-microsoft-com:vml" xmlns:o=3D"urn:schemas-microsoft-com:office:office" xmlns:p=3D"urn:schemas-microsoft-com:office:powerpoint" xmlns:oa=3D"urn:schemas-microsoft-com:office:activation" xmlns=3D"http://www.w3.org/TR/REC-html40"> <head> <meta http-equiv=3DContent-Type content=3D"text/html; charset=3Dus-ascii"> <meta name=3DProgId content=3DPowerPoint.Slide> <meta name=3DGenerator content=3D"Microsoft PowerPoint 10"> <link id=3DMain-File rel=3DMain-File href=3D"../COLTMABtalk.htm"> <link rel=3DPreview href=3Dpreview.wmf> <![if IE]> <base 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g_scaleHyperlinks=3D(document.all.tags("AREA").length>0) if( g_scaleHyperlinks ) InitHLinkArray() if( g_scaleInFrame||(IsWin("PPTSld") && parent.IsFullScrMode() ) ) document.body.scroll=3D"no" _RSW() if( IsWin("PPTSld") && parent.IsFullScrMode() ) FullScrInit(); =09 MakeSldVis(); ChkAutoAdv() if( runAnimations ) { if( document.all("NSPlay") ) document.all("NSPlay").autoStart =3D false; if( sld.filters && sld.filters.revealtrans ) setTimeout( "document.body.start()", sld.filters.revealtrans.duration * = 1000 ); else document.body.start(); } } function MakeSldVis() { var fTrans=3Dg_showAnimation && SldHasTrans() if( fTrans ) { if( g_bgSound ) { idx=3Dg_bgSound.indexOf(","); pptSound.src=3Dg_bgSound.substr( 0, idx ); pptSound.loop=3D -(parseInt(g_bgSound.substr(idx+1))); } SlideObj.filters.revealtrans.Apply() } SlideObj.style.visibility=3D"visible" if( fTrans ) SlideObj.filters.revealtrans.Play() } function MakeNotesVis() { if( !IsNts() ) return false SlideObj.style.display=3D"none" nObj =3D document.all.item("NotesObj") parent.SetHasNts(0) if( nObj ) { nObj.style.display=3D"" parent.SetHasNts(1) } return 1 } function ChkAutoAdv() { if(SldHasTrans()) SlideObj.onfilterchange=3DAutoAdv else AutoAdv() } function AutoAdv() { if(!IsWin("PPTSld") || !gUseSldTimings )return var sld=3DGetCurSld() if( (sld.mAdvDelay>0) && !parent.IsFramesMode() ) setTimeout("parent.GoToNextSld()",sld.mAdvDelay) } function GetObj(id) { if(g_supportsPPTHTML) return document.all(id); else return document.getElementById(id); } function SldHasTrans() { return SlideObj.style.getAttribute("filter")!=3D""= } function GetSldId() { return sId=3Dlocation.href.substring(location.href.la= stIndexOf('/')+1) } function HideMenu() { if( frames["PPTSld"] && PPTSld.document.all.item("ctx= tmenu") && PPTSld.ctxtmenu.style.display!=3D"none" ) { PPTSld.ctxtmenu.styl= e.display=3D'none'; return true } return false } function IsWin( name ) { return window.name =3D=3D name } function IsNts() { return IsWin("PPTNts") } function IsSldOrNts() { return( IsWin("PPTSld")||IsWin("PPTNts") ) } function SupportsPPTAnimation() { return( navigator.platform =3D=3D "Win32"= && navigator.appVersion.indexOf("Windows")>0 ) } function SupportsPPTHTML() { var appVer=3Dnavigator.appVersion, msie=3DappVer.indexOf("MSIE "), ver=3D0 if( msie >=3D 0 ) ver=3DparseFloat( appVer.substring( msie+5, appVer.indexOf(";",msie) ) ) else ver=3DparseInt(appVer) return( ver >=3D 4 && msie >=3D 0 ) } function _RSW() { if( !g_supportsPPTHTML || IsNts() || ( !g_scaleInFrame && (!IsWin("PPTSld") || !parent.IsFullScrMode()) ) ) return var padding=3D0; if( IsWin("PPTSld") && parent.IsFramesMode() ) padding=3D6 cltWidth=3Ddocument.body.clientWidth-padding cltHeight=3Ddocument.body.clientHeight-padding factor=3D(1.0*cltWidth)/g_origW if( cltHeight < g_origH*factor ) factor=3D(1.0*cltHeight)/g_origH newSize =3D g_origSz * factor if( newSize < 1 ) newSize=3D1 s=3DSlideObj.style s.fontSize=3DnewSize+"px" s.posWidth=3Dg_origW*factor s.posHeight=3Dg_origH*factor s.posLeft=3D(cltWidth-s.posWidth+padding)/2 s.posTop=3D(cltHeight-s.posHeight+padding)/2 if( g_scaleHyperlinks ) ScaleHyperlinks( factor ) } function _InitAnimations() { animRuntimeInstalled =3D ''+document.body.localTime !=3D 'undefined'; isFullScreen =3D (window.name =3D=3D "PPTSld") && !parent.IsFramesMode(); g_animUseRuntime =3D g_showAnimation && animRuntimeInstalled && !(isFullSc= reen && parent.IsSldVisited()); if( g_animUseRuntime ) { collSeq =3D document.all.tags("seq"); if( collSeq !=3D null ) { for(ii=3D0;ii<collSeq.length;ii++) { if( collSeq[ii].getAttribute( "p:nodeType" ) =3D=3D "mainSeq" ) { g_animMainSequence =3D collSeq[ii]; break; } } } if( g_animItemsToHide ) { for(jj =3D 0; jj < g_animItemsToHide.length; jj++) { if( hideObj =3D GetObj(g_animItemsToHide[jj]) ) hideObj.runtimeStyle.visibility=3D"hidden"; } } if( g_animInteractiveItems ){ for(jj =3D 0; jj < g_animInteractiveItems.length; jj++) { if( triggerObj =3D GetObj(g_animInteractiveItems[jj]) ) triggerObj.runtimeStyle.cursor=3D"hand"; } } if( gUseSldTimings && ''+g_animSlideTime !=3D 'undefined' ) { adjustedTime =3D document.body.calculateAutoAdvanceTimes( g_animSlideTim= e, g_animEffectTimings ); if( IsWin("PPTSld") && adjustedTime !=3D g_animSlideTime ) { var sld =3D GetCurSld(); sld.mAdvDelay =3D adjustedTime * 1000; } } } return g_animUseRuntime; } gSldJump =3D 0, gSldJumpTrack =3D 0, gSldJumpIdx =3D ""; function _KPH() { if( IsNts() ) return; if( !parent.IsFramesMode() && event.keyCode =3D=3D 27 && !HideMenu() ) parent.window.close( self ); else if( event.keyCode =3D=3D 32 ) { if( window.name =3D=3D "PPTSld" ) parent.PPTSld.DocumentOnClick(); else parent.GoToNextSld(); } CatchNumKeys( parent, event ); } function CatchNumKeys( win, event ) { if( win.IsFullScrMode() && (48<=3Devent.keyCode) && (event.keyCode<=3D57) = ) { gSldJump =3D 1; gSldJumpIdx +=3D (event.keyCode-48).toString(); } if( win.IsFullScrMode() && gSldJump && event.keyCode =3D=3D 13 ) { var numSlds =3D parent.GetSldList().mList.length if ( gSldJumpIdx > numSlds ) gSldJumpIdx =3D numSlds; if ( gSldJumpIdx >=3D 0 ) { if ( gSldJumpIdx =3D=3D 0 ) gSldJumpIdx =3D 1; var jumpTo =3D parseInt(gSldJumpIdx); gSldJump =3D 0; gSldJumpIdx =3D ""; win.GoToSld( parent.GetSldList().mList[jumpTo-1].mSldHref ) } } } function _KDH() { if( event.keyCode =3D=3D 8 ) { event.returnValue =3D 0; parent.GoToPrevSld(); } } function DocumentOnClick() { if( IsNts() || parent.HideMenu() ) return; if( ( g_allowAdvOnClick && !parent.IsFramesMode() ) || (event && (event.keyCode=3D=3D32) ) ) parent.GoToNextSld(); } var g_supportsPPTHTML =3D SupportsPPTHTML(), g_scaleInFrame =3D 1, gId=3D""= , g_bgSound=3D"", g_scaleHyperlinks =3D false, g_allowAdvOnClick =3D 1, g_showInBrowser = =3D 0, gLoopCont =3D 0, gUseSldTimings =3D 0; var g_showAnimation =3D g_supportsPPTHTML && SupportsPPTAnimation() && ( (w= indow.name=3D=3D"PPTSld" && !parent.IsFramesMode()) || g_showInBrowser );va= r g_animManager =3D null; var g_animUseRuntime =3D false; var g_animItemsToHide, g_animInteractiveItems, g_animSlideTime; var g_animMainSequence =3D null; var ENDSHOW_MESG=3D"End of slide show, click to exit.", SCREEN_MODE=3D"Fram= es", gIsEndShow=3D0, NUM_VIS_SLDS=3D18, SCRIPT_HREF=3D"script.js", FULLSCR_= HREF=3D"fullscreen.htm"; var gCurSld =3D gPrevSld =3D 1, g_offset =3D 0, gNtsOpen =3D gHasNts =3D gO= tlTxtExp =3D 0, gHasNarration =3D 0, gOtlOpen =3D true window.gPPTHTML=3DSupportsPPTHTML() var gMainDoc=3Dnew Array(new hrefList("slide0001.htm",1,13249,1),new hrefLi= st("slide0003.htm",1,57521,1),new hrefList("slide0005.htm",1,71169,1),new h= refList("slide0032.htm",1,99425,1),new hrefList("slide0037.htm",1,44193,1),= new hrefList("slide0039.htm",1,43633,1),new hrefList("slide0040.htm",1,1081= 45,1),new hrefList("slide0038.htm",1,87777,1),new hrefList("slide0006.htm",= 1,45857,1),new hrefList("slide0041.htm",1,50673,1),new hrefList("slide0007.= htm",1,84113,1),new hrefList("slide0045.htm",1,51105,1),new hrefList("slide= 0048.htm",1,53793,1),new hrefList("slide0042.htm",1,30865,1),new hrefList("= slide0043.htm",1,48049,1),new hrefList("slide0044.htm",1,116161,1),new href= List("slide0046.htm",1,62545,1),new hrefList("slide0047.htm",1,5633,1)); function FullScrInit() { g_allowAdvOnClick =3D GetCurSld().mAdvOnClk document.body.style.backgroundColor=3D"black" document.oncontextmenu=3Dparent._CM; document.onkeydown =3D _KDH; document.ondragstart=3DCancel document.onselectstart=3DCancel self.focus() } function Redirect( frmId ) { var str=3Ddocument.location.hash,idx=3Dstr.indexOf('#'), sId=3DGetSldId() if(idx>=3D0) str=3Dstr.substr(1); if( window.name !=3D frmId && ( sId !=3D str) ) { obj =3D GetObj("Main-File") window.location.href=3Dobj.href+"#"+sId return 1 } return 0 } var MHTMLPrefix =3D CalculateMHTMLPrefix(); function CalculateMHTMLPrefix() { if ( document.location.protocol =3D=3D 'mhtml:') { href=3Dnew String(document.location.href) Start=3Dhref.indexOf('!')+1 End=3Dhref.lastIndexOf('/')+1 if (End < Start) return href.substring(0, Start) else return href.substring(0, End) } return ''; } function GetTags(base,tag) { if(g_supportsPPTHTML) return base.all.tags(tag); else return base.getElementsByTagName(tag); } function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLP= refix+GetHrefObj( gCurSld ).mNtsHref ) } function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() } function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() } function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() } function SetHasNts( fVal ) { if( gHasNts !=3D fVal ) { gHasNts=3DfVal UpdNavPane() } } function ToggleOtlText() { gOtlTxtExp=3D!gOtlTxtExp UpdOtlPane() } function ToggleOtlPane() { frmset=3Ddocument.all("PPTHorizAdjust") frm=3Ddocument.all("PPTOtl") if( gOtlOpen ) frmset.cols=3D"*,100%" else frmset.cols=3D"25%,*" gOtlOpen=3D!gOtlOpen frm.noResize=3D!frm.noResize UpdOtNavPane() } function ToggleNtsPane() { frmset=3Ddocument.all("PPTVertAdjust") frm=3Ddocument.all("PPTNts") if( gNtsOpen ) frmset.rows=3D"100%,*" else frmset.rows=3D"*,20%" gNtsOpen=3D!gNtsOpen UpdNtsPane() } function ClearMedia() { if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0; } function FullScreen() { if ( PPTSld.g_animUseRuntime ) PPTSld.document.body.pause(); ClearMedia(); var href =3D ( document.location.protocol =3D=3D 'mhtml:') ? FULLSCR_HREF = : FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref; if(PPTNav.event.ctrlKey) { var w =3D (window.screen.availWidth * 1.0) / 2.0 var h =3D w * (PPTSld.g_origH * 1.0) / PPTSld.g_origW win =3D window.open( MHTMLPrefix+href,null,"toolbar=3D0,resizable=3D1,top= =3D0,left=3D0," + "width=3D"+ w + ",height=3D" + h ); if( PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } else { win =3D window.open( MHTMLPrefix+href,null,"fullscreen=3Dyes" ); if( PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } } function ToggleVNarration() { rObj=3DPPTSld.document.all("NSPlay") if( rObj && !PPTSld.g_animUseRuntime ) { if( (rObj.playState =3D=3D 1)||(rObj.playState =3D=3D 0) ) rObj.Play() else if( rObj.playState =3D=3D 2 ) rObj.Pause() else return; } else if( PPTSld.g_animUseRuntime ) { narObj =3D PPTSld.document.all("narrationID") if( narObj ) narObj.togglePause() } } function GetCurSldNum() { obj=3DGetHrefObj(gCurSld) if( obj.mOrigVis =3D=3D 1 ) return obj.mSldIdx else return gCurSld } function GetNumSlds() { if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 ) return GetSldList().mNumVisSlds; else return GetSldList().mList.length } function GetSldNum( href ) { for(ii=3D0; ii<GetSldList().mList.length; ii++) { if ( GetSldList().mList[ii].mSldHref =3D=3D href ) return ii+1 } return 1 } function GetHrefObj( sldIdx ){ return GetSldList().mList[sldIdx-1] } function IsFramesMode(){ return ( SCREEN_MODE =3D=3D "Frames" ) } function IsFullScrMode(){ return ( SCREEN_MODE =3D=3D "FullScreen" ) } function GoToNextSld() { ii=3DgCurSld + 1 if( GetHrefObj( ii-1 ).mOrigVis =3D=3D 0 ) { if( ii<=3DGetSldList().mList.length ) { obj=3DGetHrefObj(ii) obj.mVis=3D1 GoToSldNum(ii) return } } else { obj=3DGetHrefObj( ii ) while ( obj && ( obj.mOrigVis =3D=3D 0 ) ) obj=3DGetHrefObj(++ii) if( obj && obj.mOrigVis ) { GoToSldNum(ii) return } } if( gSldStack.length > 1 ) PopSldList(); else if( !IsFramesMode() ) { if( gLoopCont ) GoToFirst() else EndShow() } } function GoToPrevSld() { ii=3DgCurSld-1 if( ii > 0 ) { obj=3DGetHrefObj(ii) while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) ) obj=3DGetHrefObj(--ii) if( ii =3D=3D 0 ) ii=3D1 GoToSldNum(ii) } } function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) } function GoToLast() { ii=3DGetSldList().mList.length if( ii !=3D gCurSld ) GoToSld( GetHrefObj(ii).mSldHref ) } function GoToSldNum( num ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue obj =3D GetHrefObj( num ) obj.mVis=3D1 gPrevSld=3DgCurSld gCurSld =3D num; PPTSld.location.replace(MHTMLPrefix+obj.mSldHref) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function GoToSld( href ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue GetHrefObj( GetSldNum(href) ).mVis=3D1 PPTSld.location.replace(MHTMLPrefix+href) } function SldUpdated( id ) { if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return gPrevSld=3DgCurSld gCurSld=3DGetSldNum(id) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) } function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && GetHrefO= bj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) } function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) } function CloseWindow() { if( HideMenu() ) return; var event =3D PPTSld.event; if( !IsFramesMode() && event && (event.keyCode=3D=3D27 || event.keyCode=3D= =3D32 || event.type=3D=3D"click" ) ) window.close( self ); CatchNumKeys( self, event ); } function Unload() { gIsEndShow=3D0; } function SetupEndShow() { gIsEndShow=3D1; PPTSld.document.body.scroll=3D"no"; PPTSld.document.onkeypress=3DCloseWindow; PPTSld.document.onclick=3DCloseWindow; PPTSld.document.oncontextmenu=3D_CM; } function EndShow() { if( IsFramesMode() ) return if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue doc=3DPPTSld.document doc.open() doc.writeln('<html><body bgcolor=3Dblack onload=3Dparent.SetupEndShow() on= unload=3Dparent.Unload()><center><p><font face=3DTahoma color=3Dwhite size= =3D2><br><b>' + ENDSHOW_MESG + '</b></font></p></center></body></html>') doc.close() } function SetSldVisited(){ GetSldList().mList[gCurSld-1].mVisited=3Dtrue } function IsSldVisited(){ return GetSldList().mList[gCurSld-1].mVisited } function hrefList( sldHref, visible, advDelay, advClk ) { this.mSldHref=3D this.mNtsHref =3D sldHref this.mOrigVis=3D this.mVis =3D visible this.mVisited=3D false this.mAdvDelay=3D advDelay this.mAdvOnClk=3D advClk } function SldList(arr,curSld,fEnd) { this.mCurSld =3D curSld; this.mList =3D new Array(); var idx =3D 1; for(ii=3D0;ii<arr.length;ii++) { this.mList[ii] =3D new hrefList( arr[ii].mSldHref, arr[ii].mOrigVis, arr[= ii].mAdvDelay, arr[ii].mAdvOnClk ); if( arr[ii].mOrigVis ) this.mList[ii].mSldIdx =3D idx++; } this.mNumVisSlds =3D idx-1; this.fEndShow =3D fEnd; } function GetSldList() { return gSldStack[gSldStack.length-1] } function GetCurSld() { return parent.GetSldList().mList[parent.gCurSld - 1]= } gSldStack =3D new Array(); gSldStack[0] =3D new SldList(gMainDoc,gCurSld,1) function ViewCustomShow(idx,fEnd) { if( !IsFullScrMode() ) return; var sldList =3D new Array(); var custShow =3D custShowList[idx-1]; var jj =3D 0; for( ii=3D0;ii<custShow.length;ii++ ) { if( custShow[ii] <=3D gMainDoc.length ) sldList[jj++] =3D gMainDoc[custShow[ii]-1]; } if (sldList.length > 0) { PushSldList(sldList,fEnd); gCurSld =3D 1; } else if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue } function PushSldList(arr,fEnd) { var ii =3D gSldStack.length; gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd); GoToSld( gSldStack[ii].mList[0].mSldHref ); } function PopSldList() { if (gSldStack[gSldStack.length-1].fEndShow) EndShow() else { gCurSld =3D gSldStack[gSldStack.length-1].mCurSld; gSldStack[gSldStack.length-1] =3D null; gSldStack.length--; var sldList =3D gSldStack[gSldStack.length-1]; GoToSld( sldList.mList[gCurSld - 1].mSldHref ); } } var custShowList=3Dnew Array(); function ImgBtn( oId,bId,w,action ) { var t=3Dthis t.Perform =3D _IBP t.SetActive =3D _IBSetA t.SetInactive=3D _IBSetI t.SetPressed =3D _IBSetP t.SetDisabled=3D _IBSetD t.Enabled =3D _IBSetE t.ChangeIcon =3D null t.UserAction =3D action t.ChgState =3D _IBUI t.mObjId =3D oId t.mBorderId=3D bId t.mWidth =3D w t.mIsOn =3D t.mCurState =3D 0 } function _IBSetA() { if( this.mIsOn ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _IBSetI() { if( this.mIsOn ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0 } } function _IBSetP() { if( this.mIsOn ) { obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 ) obj.style.posLeft+=3D1; obj.style.posTop+=3D1 } } function _IBSetD() { obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 ) obj.style.posTop=3D0 } function _IBSetE( state ) { var t=3Dthis GetObj( t.mBorderId ).style.visibility=3D"visible" if( state !=3D t.mIsOn ) { t.mIsOn=3Dstate if( state ) t.SetInactive() else t.SetDisabled() } } function _IBP() { var t=3Dthis if( t.mIsOn ) { if( t.UserAction !=3D null ) t.UserAction() if( t.ChangeIcon ) { obj=3DGetObj(t.mObjId) if( t.ChangeIcon() ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth else obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-0)*t.mWidth } t.SetActive() } } function _IBUI( clr1,clr2,nextState ) { var t=3Dthis SetBorder( GetObj( t.mBorderId ),clr1,clr2 ) obj=3DGetObj( t.mObjId ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-obj= .style.posTop t.mCurState=3DnextState return obj } function TxtBtn( oId,oeId,action,chkState ) { var t=3Dthis t.Perform =3D _TBP t.SetActive =3D _TBSetA t.SetInactive=3D _TBSetI t.SetPressed =3D _TBSetP t.SetDisabled=3D _TBSetD t.SetEnabled =3D _TBSetE t.GetState =3D chkState t.UserAction =3D action t.ChgState =3D _TBUI t.mObjId =3D oId t.m_elementsId=3D oeId t.mIsOn =3D 1 } function _TBSetA() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gHiliteClr,gShadowClr,0,0 ) } function _TBSetI() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) } function _TBSetP() { if( this.mIsOn ) this.ChgState( gShadowClr,gHiliteClr,1,1 ) } function _TBSetD() { this.ChgState( gFaceClr,gFaceClr,0,0 ) this.mIsOn =3D 0 } function _TBSetE() { var t=3Dthis if( !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) else t.ChgState( gShadowClr,gHiliteClr,1,1 ) t.mIsOn =3D 1 } function _TBP() { var t=3Dthis if( t.mIsOn ) { if( t.UserAction !=3D null ) t.UserAction() if( !t.GetState ) return if( t.GetState() ) t.SetPressed() else t.SetActive() } } function _TBUI( clr1,clr2,lOffset,tOffset ) { SetBorder( GetObj( this.mObjId ),clr1,clr2 ) Offset( GetObj( this.m_elementsId ),lOffset,tOffset ) } function Offset( obj, top, left ){ obj.style.top=3Dtop; obj.style.left=3Dle= ft } function SetBorder( obj, upperLeft, lowerRight ) { s=3Dobj.style; s.borderStyle =3D "solid" s.borderWidth =3D 1 s.borderLeftColor =3D s.borderTopColor =3D upperLeft s.borderBottomColor=3D s.borderRightColor =3D lowerRight } function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] } function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() } function BtnOnDown(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetPressed() } function BtnOnOut(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetInactive() } function BtnOnUp() { b=3DGetBtnObj() if( b !=3D null ) b.Perform() else Upd() } function GetNtsState(){ return parent.gNtsOpen } function GetOtlState(){ return parent.gOtlOpen } function GetOtlTxtState(){ return parent.gOtlTxtExp } function NtsBtnSetFlag( fVal ) { s=3Ddocument.all.item( this.m_flagId ).style s.display=3D"none" if( fVal ) s.display=3D"" else s.display=3D"none" } function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etActive() } function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etInactive() } var gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"= THREEDFACE" var gBtnArr =3D new Array() gBtnArr["nb_otl"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPan= e,GetOtlState ) gBtnArr["nb_otlElem"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOt= lPane,GetOtlState ) gBtnArr["nb_nts"] =3D new TxtBtn( "nb_nts","nb_ntsElem",parent.ToggleNtsPan= e,GetNtsState ) gBtnArr["nb_prev"]=3D new ImgBtn( "nb_prev","nb_prevBorder",30,parent.GoToP= revSld ) gBtnArr["nb_next"]=3D new ImgBtn( "nb_next","nb_nextBorder",30,parent.GoToN= extSld ) gBtnArr["nb_sldshw"]=3D new ImgBtn( "nb_sldshw","nb_sldshwBorder",18,parent= .FullScreen ) gBtnArr["nb_sldshwBorder"] =3D new TxtBtn( "nb_sldshw","nb_sldshwBorder",pa= rent.FullScreen,null ) gBtnArr["nb_sldshwBorder"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwBorder"].SetInactive =3D _BSetI_Border; gBtnArr["nb_sldshwText"] =3D new TxtBtn( "nb_sldshw","nb_sldshwText",parent= .FullScreen,null ) gBtnArr["nb_sldshwText"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwText"].SetInactive =3D _BSetI_Border; gBtnArr["nb_voice"] =3D new ImgBtn( "nb_voice","nb_voiceBorder",18,parent.= ToggleVNarration ) gBtnArr["nb_otlTxt"]=3D new ImgBtn( "nb_otlTxt","nb_otlTxtBorder",23,parent= .ToggleOtlText ) gBtnArr["nb_nts"].m_flagId=3D "notes_flag" gBtnArr["nb_nts"].SetFlag =3D NtsBtnSetFlag gBtnArr["nb_otlTxt"].ChangeIcon=3D GetOtlTxtState var sNext=3D"Next",sPrev=3D"Previous",sEnd=3D"End Show",sFont=3D"Arial",sAr= row=3D"Arrow",sFreeform=3D"Freeform",sRect=3D"Rectangle",sOval=3D"Oval" function ShowMenu() { BuildMenu(); var doc=3DPPTSld.document.body,x=3DPPTSld.event.clientX+doc.scrollLeft,y= =3DPPTSld.event.clientY+doc.scrollTop m =3D PPTSld.document.all.item("ctxtmenu") m.style.pixelLeft=3Dx if( (x+m.scrollWidth > doc.clientWidth)&&(x-m.scrollWidth > 0) ) m.style.pixelLeft=3Dx-m.scrollWidth m.style.pixelTop=3Dy if( (y+m.scrollHeight > doc.clientHeight)&&(y-m.scrollHeight > 0) ) m.style.pixelTop=3Dy-m.scrollHeight m.style.display=3D"" } function _CM() { if( !parent.IsFullScrMode() ) return; if(!PPTSld.event.ctrlKey) { ShowMenu() return false } else HideMenu() } function BuildMenu() { if( PPTSld.document.all.item("ctxtmenu") ) return var mObj=3DCreateItem( PPTSld.document.body ) mObj.id=3D"ctxtmenu" mObj.style.visibility=3D"hidden" var s=3DmObj.style s.position=3D"absolute" s.cursor=3D"default" s.width=3D"120px" SetCMBorder(mObj,"menu","black") var iObj=3DCreateItem( mObj ) SetCMBorder( iObj, "threedhighlight","threedshadow" ) iObj.style.padding=3D2 CreateMenuItem( iObj,sNext,M_GoNextSld,M_True ) CreateMenuItem( iObj,sPrev,M_GoPrevSld,M_HasPrevSld ) CreateSeparator( iObj ) CreateMenuItem( iObj,sEnd,M_End,M_True ) mObj.style.visibility=3D"visible" } function Cancel() { window.event.cancelBubble=3Dtrue; window.event.returnVa= lue=3Dfalse } function Highlight() { ChangeClr("activecaption","threedhighlight") } function Deselect() { ChangeClr("threedface","menutext") } function Perform() { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) e.Action() else PPTSld.event.cancelBubble=3Dtrue } function ChangeClr( bg,clr ) { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) { e.style.backgroundColor=3Dbg e.style.color=3Dclr } } function M_HasPrevSld() { return( parent.HasPrevSld() ) } function M_GoNextSld() { if( gIsEndShow ) M_End(); else GoToNextSld() } function M_GoPrevSld() { if( gIsEndShow ) { history.back(); PPTSld.event.ca= ncelBubble=3Dtrue; } else GoToPrevSld() } function M_True() { return true } function M_End() { window.close( self ) } function CreateMenuItem( node,text,action,eval ) { var e=3DCreateItem( node ) e.type=3D"menuitem" e.Action=3Daction e.IsActive=3Deval e.innerHTML=3Dtext if( !e.IsActive() ) e.style.color=3D"threedshadow" e.onclick=3DPerform e.onmouseover=3DHighlight e.onmouseout=3DDeselect s=3De.style; s.fontFamily=3DsFont s.fontSize=3D"9pt" s.paddingLeft=3D2 } function CreateSeparator( node ) { var sObj=3DCreateItem( node ) SetCMBorder(sObj,"menu","menu") var s=3DsObj.style s.borderTopColor=3D"threedshadow" 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<script src=3Dscript.js></script><script><!-- if( !(IsWin("PPTOtl")||IsWin("PPTNav")||IsWin("PPTOtlNav")) ) { obj =3D GetObj("Main-File") parent.location.href=3Dobj.href } var gOtlHiliteClr=3D"#ffffff",gOtlNormalClr=3D"#000000",gOtlActiveClr=3D"#f= fff00",gSelected=3D"",gTxtState=3Dfalse,gChildEntryTable=3Dnew Array() function Load() { if( IsWin("PPTOtl" ) ){ LoadOtl(); parent.gOtlLoaded=3Dtrue; return } if( g_supportsPPTHTML ) { if( IsWin("PPTNav" ) ){ LoadNav("NavObj",UpdNav); parent.gNavLoaded=3Dtru= e; return } if( IsWin("PPTOtlNav" ) ){ LoadNav("OtlNavObj",UpdOtlNav); parent.gOtlNav= Loaded=3Dtrue; return } } } function Upd(){ if( IsWin("PPTNav") ) LoadNav("NavObj",UpdNav) } function LoadNav( oId,UpdFunc ) { document.ondragstart=3DCancelDrag document.onselectstart=3DCancelDrag document.body.style.margin=3D2 UpdFunc() obj=3Ddocument.all.item(oId) obj.style.display=3D"block" obj.style.visibility=3D"visible" document.bgColor=3D"threedface" if( parent.frames["PPTNts"] ) 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document.all.item("nb_otlTxtBorder").style.visibility =3D "hidden"; } //--></script> <style> <!--.PTxt {position:relative; width:100%; margin-top:5px; padding-left:2px; font-weight:bold;} .CTxt {position:relative; width:100%; margin-top:5px;} a {color:white; text-decoration:none;} ul {color:white; margin-bottom:0px; margin-left:20px;} .sldNum {margin-top:5px; color:white;} .button {position:absolute; width:32px; height:20px; border-style:solid; border-width:1px; border-color:threedface;} --> </style> </head> <body onload=3D"Load()" style=3D'margin:2px'> <div id=3DNavObj onload=3D"Load()" onmouseover=3D"BtnOnOver()" onmousedown=3D"BtnOnDown()" onmouseout=3D"BtnOnOut()" onmouseup=3D"BtnOnUp(= )" onkeypress=3D"_KPH()" style=3D'display:none;visibility:hidden'> <table id=3D"notesBtn" style=3D'position:absolute;display:none;width:70px' = align=3Dleft cellpadding=3D0 cellspacing=3D0> <td nowrap> <div id=3D"nb_ntsElem" align=3Dcenter style=3D'position:relative;padding:3= px; 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Outline" style=3D'position:relative;left:-157px'></div> </div> </td> </table> </div> <div id=3DOtlObj style=3D'display:none;visibility:hidden;'> <table width=3D"100%" style=3D'font-family:Arial;font-size:9pt'> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>1</font></div> </td> <td width=3D"100%"> <div id=3DPPTP1 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0001.htm');" id=3DPPTL1>Lower Bounds on = the Sample Complexity of Exploration in the Multi-Armed Bandit Problem</a></f= ont></div> <div id=3DPPTC1 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Shie Mannor</li> <li>John N. Tsitsiklis</li> <br> <br> <br> <li>Laboratory for Information and Decision Systems</li> <li>Massachusetts Institute of Technology</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>2</font></div> </td> <td> <div id=3DPPTP2 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0003.htm');" id=3DPPTL2>Problem Definiti= on</a></font></div> <div id=3DPPTC2 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Given:</li> <li>N arms.</li> <li>The reward of each arm is an IID random</li> <li>variable with unknown mean and variance.</li> <br> <br> <li>Decision maker should decide after</li> <li>some time which is the “best” arm.</li> <br> <br> <li>We consider PAC optimal strategies – strategies</li> <li>that return an ε optimal arm with probability at</li> <li>least 1- <font face=3DSymbol>d</font><font face=3DVerdana>.</font></= li> <br> <br> <br> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>3</font></div> </td> <td> <div id=3DPPTP3 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0005.htm');" id=3DPPTL3>Some History</a>= </font></div> <div id=3DPPTC3 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Some variants of MAB problem:</li> <li>Discounted, Bayesian, Markovian, expected</li> <li>reward, simultaneous (restless), and</li> <li>adversarial setups.</li> <br> <br> <li>[Jennison et. al. 82’] and [Siegmund 85’] –</li> <li>find an almost optimal arm with high</li> <li>probability for<span style=3D'mso-spacerun:yes'>       = ;    </span>.</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>4</font></div> </td> <td> <div id=3DPPTP4 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0032.htm');" id=3DPPTL4>The Upper Bound<= /a></font></div> <div id=3DPPTC4 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li><span style=3D'mso-spacerun:yes'> </span>A trivial Upper Bound = –</li> <br> <br> <br> <li>With some more work – [Even-dar et. al. 02’]</li> <br> <br> <br> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>5</font></div> </td> <td> <div id=3DPPTP5 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0037.htm');" id=3DPPTL5>The Coin Setup</= a></font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>6</font></div> </td> <td> <div id=3DPPTP6 class=3DPTxt dir=3Drtl align=3Dleft><font size=3D2><a href=3D"javascript:GoToSld('slide0039.htm');" id=3DPPTL6><span dir=3Dltr>= Objective</span></a></font></div> <div id=3DPPTC6 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>A strategy is ε-<font face=3DSymbol>d</font><font face=3DVerdan= a> correct if:</font></li> <li>It terminates w.p.1</li> <li>For any set of coins, the coin chosen is at most ε-worse than t= he best coin w.p. at least 1- <font face=3DSymbol>d</font><font face=3D= Verdana>.</font></li> <br> <br> <li>We look for a lower bound on the</li> <li>expected number of arms pulls.</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>7</font></div> </td> <td> <div id=3DPPTP7 class=3DPTxt dir=3Drtl align=3Dleft><font size=3D2><a href=3D"javascript:GoToSld('slide0040.htm');" id=3DPPTL7><span dir=3Dltr>= What can go wrong?</span></a></font></div> <div id=3DPPTC7 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Super-smart strategy.</li> <br> <br> <li>Dependence in N for N large.</li> <br> <br> <li>Dependence in ε and <font face=3DSymbol>d</font><font face=3DVe= rdana> are expected to be 1/ε<sup>2</sup><span style=3D'mso-spacerun:yes'>  </span>and<span style=3D'mso-spacerun:yes'>  </span>log(1/</font><font face=3DS= ymbol>d</font><font face=3DVerdana> ).</font></li> <br> <br> <li>Two coins – log(1/<font face=3DSymbol>d</font><font face=3DVer= dana>) / ε<sup>2</sup> [Anthony and Bartlett 99’].</font></li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>8</font></div> </td> <td> <div id=3DPPTP8 class=3DPTxt dir=3Drtl align=3Dleft><font size=3D2><a href=3D"javascript:GoToSld('slide0038.htm');" id=3DPPTL8><span dir=3Dltr>= The Main Result</span></a></font></div> <div id=3DPPTC8 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>There exists a collection of coins</li> <li> p<sub>1</sub> =3D ½ + ε, p<sub>2</sub>=3D ½ ,&#= 8230;, p<sub>N</sub>=3D ½</li> <li>such that every ε-<font face=3DSymbol>d</font><font face=3DVerd= ana> correct policy</font></li> <li>satisfies (<span style=3D'mso-spacerun:yes'>       = ;         </span>)</li> <br> <br> <br> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>9</font></div> </td> <td> <div id=3DPPTP9 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0006.htm');" id=3DPPTL9>Proof</a></font>= </div> <div id=3DPPTC9 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Define hypotheses</li> <li><span style=3D'mso-spacerun:yes'>   </span>H<sub>ℓ</= sub> :<span style=3D'mso-spacerun:yes'>     </span>p<= sub>ℓ</sub>=3D½+ε<span style=3D'mso-spacerun:yes'>   </span>;<span style=3D'mso-spacerun:yes'>     </span>p<sub>m</= sub> =3D ½<span style=3D'mso-spacerun:yes'>  </span>(m ≠ &#= 8467;)</li> <br> <br> <li><span style=3D'mso-spacerun:yes'>    </span>is the nu= mber of times coin m is sampled.</li> <br> <br> <li><span style=3D'mso-spacerun:yes'>     </span>is = the total number of heads when sampling coin m for t times.</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>10</font></div> </td> <td> <div id=3DPPTP10 class=3DPTxt dir=3Drtl align=3Dleft><font size=3D2><a href=3D"javascript:GoToSld('slide0041.htm');" id=3DPPTL10><span dir=3Dltr= >Proof (cont’)</span></a></font></div> <div id=3DPPTC10 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Consider the events:</li> <li>1.</li> <br> <br> <li>2.</li> <br> <br> <li>3.</li> <br> <br> <br> <li>where</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>11</font></div> </td> <td> <div id=3DPPTP11 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0007.htm');" id=3DPPTL11>Proof (contR= 17;)</a></font></div> <div id=3DPPTC11 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Lemma:<span style=3D'mso-spacerun:yes'>       = ;            &n= bsp;            = ;        </span>(<span style=3D'mso-spacerun:yes'>       = ;   </span>)</li> <br> <br> <li>For small δ</li> <br> <br> <br> <br> <li>Lemma:</li> <br> <br> <li>“Amount of time spent sampling m under H<sub>ℓ</sub> is<= /li> <li><span style=3D'mso-spacerun:yes'>  </span>small implies probabi= lity of choosing ℓ under</li> <li><span style=3D'mso-spacerun:yes'>  </span>H<sub>m</sub><sub> </= sub>is high.”</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>12</font></div> </td> <td> <div id=3DPPTP12 class=3DPTxt dir=3Drtl align=3Dleft><font size=3D2><a href=3D"javascript:GoToSld('slide0045.htm');" id=3DPPTL12><span dir=3Dltr= >Proof (cont’)</span></a></font></div> <div id=3DPPTC12 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Proof (of lemma):</li> <br> <br> <li>define</li> <br> <br> <br> <li>When</li> <br> <br> <li>and therefore</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>13</font></div> </td> <td> <div id=3DPPTP13 class=3DPTxt dir=3Drtl align=3Dleft><font size=3D2><a href=3D"javascript:GoToSld('slide0048.htm');" id=3DPPTL13><span dir=3Dltr= >Proof (cont’)</span></a></font></div> <div id=3DPPTC13 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>When<span style=3D'mso-spacerun:yes'>     &= nbsp; </span>holds, under H<sub>ℓ</sub><sub> </sub>:</li> <br> <br> <li>For each sample path the coins behave as predicted by their p's.</li> <li>Correctness implies that for most such paths hypothesis H<sub>ℓ= ;</sub> is chosen.</li> <li>Under hypothesis H<sub>m</sub> :</li> <li>Such paths have δ <span style=3D'mso-spacerun:yes'> </span>probability (proved by bound= ing likelihood ratio).</li> <li>H<sub>ℓ</sub> is again selected.</li> <li> <span style=3D'mso-spacerun:yes'>   </span> <span style=3D'mso-spacerun:yes'>    </span>□</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>14</font></div> </td> <td> <div id=3DPPTP14 class=3DPTxt dir=3Drtl align=3Dleft><font size=3D2><a href=3D"javascript:GoToSld('slide0042.htm');" id=3DPPTL14><span dir=3Dltr= >Proof (cont’)</span></a></font></div> <div id=3DPPTC14 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Since the policy is ε-<font face=3DSymbol>d</font><font face=3D= Verdana> correct and</font></li> <br> <br> <br> <li>We have that<span style=3D'mso-spacerun:yes'>       = ;         </span>for all</li> <br> <br> <li>Result follows by summing over</li> <li><span dir=3Drtl><span dir=3Dltr>□</span></span></li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>15</font></div> </td> <td> <div id=3DPPTP15 class=3DPTxt dir=3Drtl align=3Dleft><font size=3D2><a href=3D"javascript:GoToSld('slide0043.htm');" id=3DPPTL15><span dir=3Dltr= >The Bayesian Setup</span></a></font></div> <div id=3DPPTC15 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>A weaker notion of optimality:</li> <li>A strategy is ε-<font face=3DSymbol>d</font><font face=3DVerdan= a> correct with respect</font></li> <li>to a prior p (on the biases) if:</li> <li>It terminates w.p.1</li> <li>W.p. at least 1- <font face=3DSymbol>d</font><font face=3DVerdana> (= w.r.t. the prior) the coin chosen is at most ε-worse than the best coi= n.</font></li> <br> <br> <li>A similar result holds.</li> <br> <br> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>16</font></div> </td> <td> <div id=3DPPTP16 class=3DPTxt dir=3Drtl align=3Dleft><font size=3D2><a href=3D"javascript:GoToSld('slide0044.htm');" id=3DPPTL16><span dir=3Dltr= >The case of given biases</span></a></font></div> <div id=3DPPTC16 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Suppose we want to bound the</li> <li>exploration time for a given set of</li> <li>biases, but unknown to the decision</li> <li>maker (p* is the best coin).</li> <li>Then every ε-<font face=3DSymbol>d</font><font face=3DVerdana> = correct policy satisfies:</font></li> <br> <br> <br> <br> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>17</font></div> </td> <td> <div id=3DPPTP17 class=3DPTxt dir=3Drtl align=3Dleft><font size=3D2><a href=3D"javascript:GoToSld('slide0046.htm');" id=3DPPTL17><span dir=3Dltr= >Conclusions</span></a></font></div> <div id=3DPPTC17 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>The complexity is</li> <br> <br> <li>We don’t gain much by dynamic decisions.</li> <br> <br> <li>Bayesian/permutations setup.</li> <br> <br> <li>Results can be extended to richer random</li> <li>variables.</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>18</font></div> </td> <td> <div id=3DPPTP18 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0047.htm');" id=3DPPTL18>Lower Bounds on= the Sample Complexity of Exploration in the Multi-Armed Bandit Problem</a></f= ont></div> <div id=3DPPTC18 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Shie Mannor</li> <li>John N. Tsitsiklis</li> <br> <br> <li>Laboratory for Information and Decision Systems</li> <li>Massachusetts Institute of Technology</li> </ul> </font></div> </td> </tr> </table> </div> <div style=3D'display:none'><a href=3D"../COLTMABtalk.htm"></a><a href=3Dmaster06.htm></a><a href=3Dmaster06.xml></a><a href=3Dpreview.wmf></= a><a href=3Dmaster07.htm></a><a href=3Dmaster07.xml></a><a href=3Dmaster02.htm><= /a><a href=3Dpres.xml></a><a href=3Dslide0001.htm></a><a href=3D"master07_image00= 1.gif"></a><a href=3Dslide0003.htm></a><a href=3D"master06_image002.gif"></a><a href=3Dslide0005.htm></a><a href=3D"slide0005_image003.wmz"></a><a href=3D"slide0005_image004.gif"></a><a href=3Dslide0032.htm></a><a href=3D"slide0032_image005.wmz"></a><a href=3D"slide0032_image006.gif"></a>= <a href=3D"slide0032_image007.wmz"></a><a href=3D"slide0032_image008.gif"></a>= <a href=3Dslide0037.htm></a><a href=3Dslide0039.htm></a><a href=3Dslide0040.ht= m></a><a href=3Dslide0038.htm></a><a 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