Discrete Mathematics and Optimization Seminar
Feb. 22nd, 2010
Multi-Armed Bandits in Metric Spaces
Alex Slivkins
Microsoft Research
In a multi-armed bandit problem, an online algorithm chooses from a fixed set of alternatuves (a.k.a. "strategies" or "arms") in a sequence of trials so as to maximize the total payoff of the chosen strategies. While the performance of bandit algorithms with a small finite strategy set is quite well understood, bandit problems with large strategy sets are still a topic of very active investigation, motivated by practical applications such as online auctions and web advertisement. The goal of such research is to identify broad and natural classes of strategy sets and payoff functions which enable the design of efficient solutions. In this work we study a very general setting for the multi-armed bandit problem in which the strategies form a metric space, and the payoff function satisfies a Lipschitz condition with respect to the metric.

Joint work with Bobby Kleinberg and Eli Upfal.
Based on papers in STOC'08 and SODA'10 and some recent work.