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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72" style='word-wrap:break-word'><div class=WordSection1><p class=MsoNormal><b><i><span style='font-size:14.0pt'>In-Person seminars will be held at Dunham Lab, 10 Hillhouse Ave., Room 220, with an option of remote participation via zoom.<o:p></o:p></span></i></b></p><p class=MsoNormal><b><u><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'><a href="x-apple-data-detectors://10/"><span style='color:black'>3:30pm</span></a> - Pre-talk meet and greet, Suite 222, Room 228</span></u></b><b><i><o:p></o:p></i></b></p><p class=MsoNormal style='background:white'><span style='color:black'><a href="https://statistics.yale.edu/" title="Department of Statistics and Data Science
"><span style='font-size:22.0pt;font-family:"Lucida Sans",sans-serif;color:#286DC0;text-decoration:none'><img border=0 width=150 height=49 style='width:1.5625in;height:.5104in' id=logo src="cid:image001.jpg@01D8E38D.11FAE9A0" alt="Department of Statistics and Data Science
"></span></a> <a href="https://statistics.yale.edu/" title=Home><b><span style='font-size:22.0pt;font-family:"Lucida Sans",sans-serif;color:#286DC0'>Department of Statistics and Data Science </span></b></a></span><b><i><u><span style='font-size:22.0pt;font-family:"Lucida Sans",sans-serif;color:#286DC0'> <o:p></o:p></span></u></i></b></p><p class=MsoNormal style='margin-top:.1in'><i><u><span style='font-size:16.0pt;font-family:"Arial",sans-serif'>We invite you to attend our in-person seminar.</span></u></i><span style='font-size:13.0pt;font-family:"Arial",sans-serif;background:white'><o:p></o:p></span></p><p class=MsoNormal style='margin-top:.1in'><span style='font-size:14.0pt;font-family:"Arial",sans-serif'><a href="https://statistics.yale.edu/seminars/qiaomin-xie"><span style='color:windowtext;text-decoration:none'>Qiaomin Xie</span></a>, University of Wisconsin-Madison<o:p></o:p></span></p><p class=MsoNormal><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
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</v:shape><![endif]--><![if !vml]><img width=154 height=185 style='width:1.6041in;height:1.927in' src="cid:image004.jpg@01D8E78C.3C96C0A0" align=left hspace=12 v:shapes="Picture_x0020_4"><![endif]><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>In-Person<o:p></o:p></span></b></p><p class=MsoNormal><span class=date-display-single><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Monday, October 24, 2022</span><o:p></o:p></span></p><p class=MsoNormal><span class=date-display-start><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>4:00PM</span></span><span class=date-display-range><span style='font-size:12.0pt;font-family:"Arial",sans-serif'> to </span></span><span class=date-display-end><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>5:00PM</span></span><o:p></o:p></p><p class=MsoNormal><span class=fn><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Dunham Lab. Room 220</span></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif'> <span class=map-icon><span style='letter-spacing:.6pt'><a href="http://maps.google.com/?q=10+Hillhouse+Avenue%2C+New+Haven%2C+CT%2C+06511%2C+us"><span style='color:windowtext'>see map</span></a> </span></span><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>10 Hillhouse Avenue<o:p></o:p></span></p><p class=MsoNormal><span class=locality><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>New Haven</span></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>, <span class=region>CT</span> <span class=postal-code>06511</span><o:p></o:p></span></p><p class=MsoNormal><span class=MsoHyperlink><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><a href="https://qiaominxie.github.io/">Website</a></span><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></p><p class=MsoNormal><strong><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Zoom Link: </span></strong><strong><span style='font-family:"Calibri",sans-serif'><o:p></o:p></span></strong></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><a href="https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09">https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09</a> / Password: 24<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal style='background:white'><b><span style='font-size:15.0pt;font-family:Mallory;color:#222222;mso-fareast-language:EN-US'>Title: Markovian Linear Stochastic Approximation: Bias and Extrapolation<o:p></o:p></span></b></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><b><span style='font-size:13.0pt;font-family:Mallory;color:#222222;mso-fareast-language:EN-US'>Information and Abstract: <o:p></o:p></span></b></p><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-size:13.0pt;font-family:Mallory;color:#222222;mso-fareast-language:EN-US'>We consider Linear Stochastic Approximation (LSA) with a constant stepsize and Markovian data. Viewing the LSA iterate as a Markov chain, we prove its convergence to a unique stationary distribution in Wasserstein distance and establish non-asymptotic, geometric convergence rates. Furthermore, we show that the bias vector of this limit admits an infinite series expansion w.r.t. the stepsize, and hence the bias is proportional to the stepsize up to higher order terms. This result stands in contrast with LSA under i.i.d. data, for which the bias vanishes. In fact, we show that the bias scales with the mixing time of the Markovian data. With the above characterization, one can employ Richardson-Romberg extrapolation with m stepsizes to eliminate the m−1 leading terms in the bias expansion, resulting in an exponentially smaller bias.<o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-size:13.0pt;font-family:Mallory;color:#222222;mso-fareast-language:EN-US'>The above results give a recipe for approaching the best of three worlds: (1) use a constant stepsize to achieve fast, geometric convergence of the optimization error, (2) average the iterates to eliminate the asymptotic variance, and (3) employ extrapolation to order-wise reduce the asymptotic bias. Our results immediately apply to the Temporal Difference learning algorithm with linear function approximation.<o:p></o:p></span></p><p class=MsoNormal style='line-height:18.0pt;background:white'><b><u><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'><a href="x-apple-data-detectors://10/"><span style='color:black'>3:30pm</span></a> - Pre-talk meet and greet, room 222</span></u></b><b><u><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p></o:p></span></u></b></p><p class=MsoNormal><strong><span style='font-family:"Calibri",sans-serif'><o:p> </o:p></span></strong></p><p class=MsoNormal><strong><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Zoom Link: </span></strong><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Join from PC, Mac, Linux, iOS or Android: <a href="https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09">https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09</a> </span><o:p></o:p></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Password: 24<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Or Telephone</span><span lang=JA style='font-size:12.0pt;font-family:"MS Gothic"'>：</span><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>203-432-9666 (2-ZOOM if on-campus) or 646 568 7788<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Meeting ID: 924 1107 7917<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.5pt'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.5pt'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.5pt'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.5pt'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.5pt'><o:p> </o:p></span></p><h2 style='margin:0in;box-sizing: inherit;font-feature-settings: "kern", "liga", "dlig"'><span style='font-family:"Georgia",serif;font-weight:normal'>Department of Statistics and Data Science<o:p></o:p></span></h2><p style='margin:0in;box-sizing: inherit'><span style='font-size:9.0pt;color:black'>Yale University<br>24 Hillhouse Avenue<br>New Haven, CT 06511<o:p></o:p></span></p><p style='margin:0in;box-sizing: inherit'><span style='font-size:9.0pt;color:black'>t 203.432.0666<br>f 203.432.0633<o:p></o:p></span></p><p class=MsoNormal><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></b></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>