Robust Batch Policy Learning in Markov Decision Processes

We consider a varying horizon Markov decision process (MDP), where each policy is evaluated by a set containing average rewards over different horizon lengths with different reference distributions. 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 approximately maximize the smallest value of this set. Leveraging semi-parametric statistics, we develop an efficient policy learning method for estimating the defined robust optimal policy that can efficiently break the curse of horizon. A rate-optimal regret bound up to a logarithmic factor is established in terms of the number of trajectories and the number of decision points. Our regret guarantee subsumes the long-term average reward MDP setting as a special case.