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.

翻译：批量强化学习旨在利用预收集的数据找到最优策略，以最大化动态环境中的期望总奖励。几乎所有现有算法都依赖于目标策略诱导分布相对于数据分布的绝对连续性假设，从而通过测度变换利用批量数据校正目标策略。然而，在实际应用中（例如支持集无重叠情况），特别是在状态-动作空间较大或连续时，绝对连续性假设可能被违反。本文针对连续状态和动作的无限时域马尔可夫决策过程，提出一种无需绝对连续性假设的批量强化学习算法，命名为STEEL（奇异性感知强化学习）。该算法源于离策略评估的新型误差分析：我们利用最大均值差异结合分布鲁棒优化，刻画由潜在奇异性导致的离策略评估误差，并实现模型外推。通过引入悲观思想并在温和条件下，我们为所提算法推导了有限样本遗憾保证，且无需绝对连续性假设。与现有算法相比，STEEL仅需最低限度的数据覆盖假设，显著提升了批量强化学习的适用性和鲁棒性。大量仿真实验及一项个性化定价真实实验表明，该方法在处理批量强化学习中的潜在奇异性方面具有优越性能。