Improved Exploration in Factored Average-Reward MDPs

Sadegh Talebi (1) , Anders Jonsson (2) , Odalric-Ambrym Maillard (3, 4, 5)

1 UCPH - University of Copenhagen = Københavns Universitet
2 UPF - Universitat Pompeu Fabra [Barcelona]
3 Inria Lille - Nord Europe
4 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
5 Scool - Scool

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 stateaction space X and the state-space S admit the respective factored forms of X = ⊗ n i=1 X i and S = ⊗ m i=1 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 that have frequentist regret guarantees.

Domaines: Intelligence artificielle [cs.AI]; Machine Learning [stat.ML]

Sadegh Talebi, Anders Jonsson, Odalric-Ambrym Maillard. Improved Exploration in Factored Average-Reward MDPs. 24th International Conference on Artificial Intelligence and Statistics, 2021, San diego (virtual), United States. ⟨hal-03780564⟩