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Offline reinforcement learning (RL) aims at learning an optimal strategyusing a pre-collected dataset without further interactions with theenvironment. While various algorithms have been proposed for offline RL in theprevious literature, the minimax optimality has only been (nearly) establishedfor tabular Markov decision processes (MDPs). In this paper, we focus onoffline RL with linear function approximation and propose a new pessimism-basedalgorithm for offline linear MDP. At the core of our algorithm is theuncertainty decomposition via a reference function, which is new in theliterature of offline RL under linear function approximation. Theoreticalanalysis demonstrates that our algorithm can match the performance lower boundup to logarithmic factors. We also extend our techniques to the two-playerzero-sum Markov games (MGs), and establish a new performance lower bound forMGs, which tightens the existing result, and verifies the nearly minimaxoptimality of the proposed algorithm. To the best of our knowledge, these arethe first computationally efficient and nearly minimax optimal algorithms foroffline single-agent MDPs and MGs with linear function approximation.

Nearly Minimax Optimal Offline Reinforcement Learning with Linear Function Approximation: Single-Agent MDP and Markov Game