Nearly Minimax Optimal Offline Reinforcement Learning with Linear Function Approximation: Single-Agent MDP and Markov Game
This provides computationally efficient and nearly optimal solutions for offline RL in linear settings, addressing a gap in theoretical guarantees for both single-agent and multi-agent scenarios.
The paper tackles offline reinforcement learning with linear function approximation by proposing a pessimism-based algorithm for single-agent MDPs and two-player zero-sum Markov games, achieving performance that matches the lower bound up to logarithmic factors, establishing nearly minimax optimality.
Offline reinforcement learning (RL) aims at learning an optimal strategy using a pre-collected dataset without further interactions with the environment. While various algorithms have been proposed for offline RL in the previous literature, the minimax optimality has only been (nearly) established for tabular Markov decision processes (MDPs). In this paper, we focus on offline RL with linear function approximation and propose a new pessimism-based algorithm for offline linear MDP. At the core of our algorithm is the uncertainty decomposition via a reference function, which is new in the literature of offline RL under linear function approximation. Theoretical analysis demonstrates that our algorithm can match the performance lower bound up to logarithmic factors. We also extend our techniques to the two-player zero-sum Markov games (MGs), and establish a new performance lower bound for MGs, which tightens the existing result, and verifies the nearly minimax optimality of the proposed algorithm. To the best of our knowledge, these are the first computationally efficient and nearly minimax optimal algorithms for offline single-agent MDPs and MGs with linear function approximation.