Piecewise-Stationary Bandit Problems with Side Information

author: Jia Yuan Yu, Electrical and Computer Engineering Department, McGill University
published: Aug. 26, 2009,   recorded: June 2009,   views: 3124


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We consider a sequential decision problem where the rewards are generated by a piecewise-stationary distribution. However, the different reward distributions are unknown and may change at unknown instants. Our approach uses a limited number of side observations on past rewards, but does not require prior knowledge of the frequency of changes. In spite of the adversarial nature of the reward process, we provide an algorithm whose regret, with respect to the baseline with perfect knowledge of the distributions and the changes, is O(k log(T)), where k is the number of changes up to time T. This is in contrast to the case where side observations are not available, and where the regret is at least Ω(√T). We also show that our bound is tight for a natural class of algorithms. An earlier version of this work appears in [YM09].

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