Multi-Armed Bandits in Metric Spaces

In a multi-armed bandit problem, an online algorithm chooses from a set of strategies in a sequence of n 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 multiarmed bandit problem in which the strategies form a metric space, and the payoff function satisfies a Lipschitz condition with respect to the metric. We refer to this problem as the Lipschitz MAB problem. We present a complete solution for the multi-armed problem in this setting. That is, for every metric space (L, X) we define an isometry...

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Robert Kleinberg, Aleksandrs Slivkins, Eli Upfal
• Keywords: Bandit, Bandit Problem, CORR 2008, Education, Payoff Functions