ModelBased Reinforcement Learning Exploiting StateAction Equivalence
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Proceedings of The Eleventh Asian Conference on Machine Learning, PMLR 101:204219, 2019.
Abstract
Leveraging an equivalence property in the statespace of a Markov Decision Process (MDP) has been investigated in several studies. This paper studies equivalence structure in the reinforcement learning (RL) setup, where transition distributions are no longer assumed to be known. We present a notion of similarity between transition probabilities of various stateaction pairs of an MDP, which naturally defines an equivalence structure in the stateaction space. We present equivalenceaware confidence sets for the case where the learner knows the underlying structure in advance. These sets are provably smaller than their corresponding equivalenceoblivious counterparts. In the more challenging case of an unknown equivalence structure, we present an algorithm called ApproxEquivalence that seeks to find an (approximate) equivalence structure, and define confidence sets using the approximate equivalence. To illustrate the efficacy of the presented confidence sets, we present CUCRL, as a natural modification of UCRL2 for RL in undiscounted MDPs. In the case of a known equivalence structure, we show that CUCRL improves over UCRL2 in terms of \emph{regret} by a factor of $\sqrt{SA/C}$, in any communicating MDP with $S$ states, $A$ actions, and $C$ classes, which corresponds to a massive improvement when $C\ll SA$. To the best of our knowledge, this is the first work providing regret bounds for RL when an equivalence structure in the MDP is efficiently exploited. In the case of an unknown equivalence structure, we show through numerical experiments that CUCRL combined with ApproxEquivalence outperforms UCRL2 in ergodic MDPs.
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