Overcoming the Curse of Dimensionality in Reinforcement Learning Through Approximate Factorization

Abstract

Factored Markov Decision Processes (FMDPs) offer a promising framework for overcoming the curse of dimensionality in reinforcement learning (RL) by decomposing high-dimensional MDPs into smaller and independently evolving components. Despite their potential, existing studies on FMDPs face three key limitations: reliance on perfectly factorizable models, suboptimal sample complexity guarantees for model-based algorithms, and the absence of model-free algorithms. To address these challenges, we introduce approximate factorization, which extends FMDPs to handle imperfectly factored models. Moreover, we develop a model-based algorithm and a model-free algorithm (in the form of variance-reduced Q-learning), both achieving the first near-minimax sample complexity guarantees for FMDPs. A key novelty in the design of these two algorithms is the development of a graph-coloring-based optimal synchronous sampling strategy. Numerical simulations based on the wind farm storage control problem corroborate our theoretical findings.