Improved Exploration in Factored Average-Reward MDPs
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We consider a regret minimization task under the average-reward criterion in an unknown Factored Markov Decision Process (FMDP). More specifically, we consider an FMDP where the state-action space 𝒳 and the state-space 𝒮 admit the respective factored forms of 𝒳 = ⊗_i=1^n 𝒳_i and 𝒮=⊗_i=1^m 𝒮_i, and the transition and reward functions are factored over 𝒳 and 𝒮. Assuming known factorization structure, we introduce a novel regret minimization strategy inspired by the popular UCRL2 strategy, called DBN-UCRL, which relies on Bernstein-type confidence sets defined for individual elements of the transition function. We show that for a generic factorization structure, DBN-UCRL achieves a regret bound, whose leading term strictly improves over existing regret bounds in terms of the dependencies on the size of 𝒮_i's and the involved diameter-related terms. We further show that when the factorization structure corresponds to the Cartesian product of some base MDPs, the regret of DBN-UCRL is upper bounded by the sum of regret of the base MDPs. We demonstrate, through numerical experiments on standard environments, that DBN-UCRL enjoys a substantially improved regret empirically over existing algorithms.
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