STEEL: Singularity-aware Reinforcement Learning

Batch reinforcement learning (RL) aims at leveraging pre-collected data to find an optimal policy that maximizes the expected total rewards in a dynamic environment. Nearly all existing algorithms rely on the absolutely continuous assumption on the distribution induced by target policies with respect to the data distribution, so that the batch data can be used to calibrate target policies via the change of measure. However, the absolute continuity assumption could be violated in practice (e.g., no-overlap support), especially when the state-action space is large or continuous. In this paper, we propose a new batch RL algorithm without requiring absolute continuity in the setting of an infinite-horizon Markov decision process with continuous states and actions. We call our algorithm STEEL: SingulariTy-awarE rEinforcement Learning. Our algorithm is motivated by a new error analysis on off-policy evaluation, where we use maximum mean discrepancy, together with distributionally robust optimization, to characterize the error of off-policy evaluation caused by the possible singularity and to enable model extrapolation. By leveraging the idea of pessimism and under some mild conditions, we derive a finite-sample regret guarantee for our proposed algorithm without imposing absolute continuity. Compared with existing algorithms, by requiring only minimal data-coverage assumption, STEEL significantly improves the applicability and robustness of batch RL. Extensive simulation studies and one real experiment on personalized pricing demonstrate the superior performance of our method in dealing with possible singularity in batch RL.