<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">DEPARTMENT OF COMPUTER SCIENCE<div><br class="webkit-block-placeholder"></div><div>UNIVERSITY OF CHICAGO</div><div><br class="webkit-block-placeholder"></div><div>Date: Monday, March 31, 2008</div><div>Time: 2:30 p.m.</div><div>Place: Ryerson 251, 1100 E. 58th Street</div><div><br class="webkit-block-placeholder"></div><div>----------------------------------------------------------</div><div><br class="webkit-block-placeholder"></div><div>Speaker:<span class="Apple-tab-span" style="white-space: pre; "> </span>Alexander Rakhlin</div><div><br class="webkit-block-placeholder"></div><div>From:<span class="Apple-tab-span" style="white-space: pre; "> </span>University of California - Berkeley</div><div><br class="webkit-block-placeholder"></div><div>Web page:<span class="Apple-tab-span" style="white-space: pre; "> <a href="http://www.cs.princeton.edu/~frances/">http://www.eecs.berkeley.edu/~rakhlin/</a></span></div><div><br class="webkit-block-placeholder"></div><div>Title: Online Learning with Limited Feedback</div><div><br class="webkit-block-placeholder"></div><div>Abstract: One’s ability to learn and make decisions rests heavily on the availability of feedback. In sequential decision-making problems such feedback is often limited. A gambler, for example, can observe entirely the outcome of a horse race regardless of where he place is bet; however, when the same gambler chooses his route to travel to the race track, perhaps at a busy hour, he will likely never learn the outcome of possible alternatives. The latter limited-feedback problem is the focus of this talk. </div><p class="MsoNormal"><o:p></o:p></p><p class="MsoNormal">The problem can be phrased as an Online Linear Optimization game with “bandit” feedback. The existence of a low-regret algorithm has been an open question since the work of Awerbuch and Kleinberg in 2004. A recent reduction to the multi-armed bandit problem allowed Dani, Hayes, and Kakade to achieve a low-regret guarantee, unfortunately at the expense of computational efficiency. We present the first known efficient low-regret algorithm for bandit Online Linear Optimization over arbitrary convex decision sets. We show how the difficulties encountered by previous approaches are overcome by employing regularization. Our solution reveals surprising connections between online learning and Interior Point methods in Optimization. We also discuss an emerging phenomenon: regret guarantees for stochastic and adversarial settings turn out to be the same. </p><p class="MsoNormal"><o:p></o:p></p><p class="MsoNormal">In particular, our method solves the Online Shortest Path problem: at each round, a path from source to sink is chosen and only the total length (delay) of this path is revealed. A low-regret algorithm for this problem has applications in network routing, resource allocation, dynamic treatment of patients, and more. The worst-case guarantees enjoyed by our method imply robustness with respect to noise and malicious adversary. </p><p class="MsoNormal"><o:p></o:p></p><p class="MsoNormal">Joint work with Jacob Abernethy and Elad Hazan.<span style="font-size: 11pt; font-family: Helvetica; "><o:p></o:p></span></p><p class="MsoNormal">---------------------------------------------------------</p><p class="MsoNormal">Host:<span class="Apple-tab-span" style="white-space: pre; "> </span>Partha Niyogi</p></body></html>