[Colloquium] Talk by Alexander Rakhlin, University of California - Berkeley on Wednesday, April 2, 2008

[caseyk]

DEPARTMENT OF COMPUTER SCIENCE

UNIVERSITY OF CHICAGO

Date: Wednesday, April 2, 2008
Time: 2:30 p.m.
Place: Ryerson 251, 1100 E. 58th Street

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Speaker:	Alexander Rakhlin

From:		University of California - Berkeley

Web page:	http://www.eecs.berkeley.edu/~rakhlin/

Title: Online Learning with Limited Feedback

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.

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.


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.


Joint work with Jacob Abernethy and Elad Hazan.

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Host:	Partha Niyogi
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