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Adaptive Sampling for Best Policy Identification in Markov Decision Processes

Aymen Al Marjani · Alexandre Proutiere

[ Abstract ] [ Livestream: Visit Learning Theory 14 ] [ Paper ]
Thu 22 Jul 6:30 a.m. — 6:35 a.m. PDT

We investigate the problem of best-policy identification in discounted Markov Decision Processes (MDPs) when the learner has access to a generative model. The objective is to devise a learning algorithm returning the best policy as early as possible. We first derive a problem-specific lower bound of the sample complexity satisfied by any learning algorithm. This lower bound corresponds to an optimal sample allocation that solves a non-convex program, and hence, is hard to exploit in the design of efficient algorithms. We then provide a simple and tight upper bound of the sample complexity lower bound, whose corresponding nearly-optimal sample allocation becomes explicit. The upper bound depends on specific functionals of the MDP such as the sub-optimality gaps and the variance of the next-state value function, and thus really captures the hardness of the MDP. Finally, we devise KLB-TS (KL Ball Track-and-Stop), an algorithm tracking this nearly-optimal allocation, and provide asymptotic guarantees for its sample complexity (both almost surely and in expectation). The advantages of KLB-TS against state-of-the-art algorithms are discussed and illustrated numerically.

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