Offline reinforcement learning (RL) aims to find optimal policies in dynamic environments in order to maximize the expected total rewards by leveraging pre-collected data. Learning from heterogeneous data is one of the fundamental challenges in offline RL. Traditional methods focus on learning an optimal policy for all individuals with pre-collected data from a single episode or homogeneous batch episodes, and thus, may result in a suboptimal policy for a heterogeneous population. In this paper, we propose an individualized offline policy optimization framework for heterogeneous time-stationary Markov decision processes (MDPs). The proposed heterogeneous model with individual latent variables enables us to efficiently estimate the individual Q-functions, and our Penalized Pessimistic Personalized Policy Learning (P4L) algorithm guarantees a fast rate on the average regret under a weak partial coverage assumption on behavior policies. In addition, our simulation studies and a real data application demonstrate the superior numerical performance of the proposed method compared with existing methods.

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