Robust Batch Policy Learning in Markov Decision Processes

We study the offline data-driven sequential decision making problem in the framework of Markov decision process (MDP). In order to enhance the generalizability and adaptivity of the learned policy, we propose to evaluate each policy by a set of the average rewards with respect to distributions centered at the policy induced stationary distribution. Given a pre-collected dataset of multiple trajectories generated by some behavior policy, our goal is to learn a robust policy in a pre-specified policy class that can maximize the smallest value of this set. Leveraging the theory of semi-parametric statistics, we develop a statistically efficient policy learning method for estimating the de ned robust optimal policy. A rate-optimal regret bound up to a logarithmic factor is established in terms of total decision points in the dataset.