On the Role of General Function Approximation in Offline Reinforcement Learning

We study offline reinforcement learning (RL) with general function approximation. General function approximation is a powerful tool for algorithm design and analysis, but its adaptation to offline RL encounters several challenges due to varying approximation targets and assumptions that blur the real meanings of function assumptions. In this paper, we try to formulate and clarify the treatment of general function approximation in offline RL in two aspects: (1) analyzing different types of assumptions and their practical usage, and (2) understanding its role as a restriction on underlying MDPs from information-theoretic perspectives. Additionally, we introduce a new insight for lower bound establishing: one can exploit modelrealizability to establish general-purpose lower bounds that can be generalized into other functions. Building upon this insight, we propose two generic lower bounds that contribute to a better understanding of offline RL with general function approximation.