Efficient BiasSpanConstrained ExplorationExploitation in Reinforcement Learning
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Proceedings of the 35th International Conference on Machine Learning, PMLR 80:15781586, 2018.
Abstract
We introduce SCAL, an algorithm designed to perform efficient explorationexploration in any unknown weaklycommunicating Markov Decision Process (MDP) for which an upper bound c on the span of the optimal bias function is known. For an MDP with $S$ states, $A$ actions and $\Gamma \leq S$ possible next states, we prove a regret bound of $O(c\sqrt{\Gamma SAT})$, which significantly improves over existing algorithms (e.g., UCRL and PSRL), whose regret scales linearly with the MDP diameter $D$. In fact, the optimal bias span is finite and often much smaller than $D$ (e.g., $D=+\infty$ in noncommunicating MDPs). A similar result was originally derived by Bartlett and Tewari (2009) for REGAL.C, for which no tractable algorithm is available. In this paper, we relax the optimization problem at the core of REGAL.C, we carefully analyze its properties, and we provide the first computationally efficient algorithm to solve it. Finally, we report numerical simulations supporting our theoretical findings and showing how SCAL significantly outperforms UCRL in MDPs with large diameter and small span.
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