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Maximin Action Identification: A New Bandit Framework for Games

Abstract

We study an original problem of pure exploration in a strategic bandit model motivated by Monte Carlo Tree Search. It consists in identifying the best action in a game, when the player may sample random outcomes of sequentially chosen pairs of actions. We propose two strategies for the fixed-confidence setting: Maximin-LUCB, based on lower-and upper-confidence bounds; and Maximin-Racing, which operates by successively eliminating the sub-optimal actions. We discuss the sample complexity of both methods and compare their performance empirically. We sketch a lower bound analysis, and possible connections to an optimal algorithm.
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Dates and versions

hal-01273842 , version 1 (14-02-2016)
hal-01273842 , version 2 (21-11-2016)

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Aurélien Garivier, Emilie Kaufmann, Wouter M. Koolen. Maximin Action Identification: A New Bandit Framework for Games. 29th Annual Conference on Learning Theory (COLT), Jun 2016, New-York, United States. ⟨hal-01273842v2⟩
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