Improved Exploration in Factored Average-Reward MDPs

• URL: http://arxiv.org/abs/2009.04575v3
• Date: Thu, 11 Mar 2021 13:01:24 GMT
• Title: Improved Exploration in Factored Average-Reward MDPs
• Authors: Mohammad Sadegh Talebi, Anders Jonsson, Odalric-Ambrym Maillard
• Abstract summary: We consider a regret minimization task under the average-reward criterion in an unknown Factored Markov Decision Process (FMDP) 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 $mathcal S_i$'s and the involved diameter-related terms.
• Score: 23.096751699592133
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $\mathcal X$ and the state-space $\mathcal S$ admit the respective factored forms of $\mathcal X = \otimes_{i=1}^n \mathcal X_i$ and $\mathcal S=\otimes_{i=1}^m \mathcal S_i$, and the transition and reward functions are factored over $\mathcal X$ and $\mathcal S$. 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 $\mathcal S_i$'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 substantially improved regret empirically over existing algorithms that have frequentist regret guarantees.

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