This paper investigates model robustness in reinforcement learning (RL) to reduce the sim-to-real gap in practice. We adopt the framework of distributionally robust Markov decision processes (RMDPs), aimed at learning a policy that optimizes the worst-case performance when the deployed environment falls within a prescribed uncertainty set around the nominal MDP. Despite recent efforts, the sample complexity of RMDPs remained mostly unsettled regardless of the uncertainty set in use. It was unclear if distributional robustness bears any statistical consequences when benchmarked against standard RL. Assuming access to a generative model that draws samples based on the nominal MDP, we characterize the sample complexity of RMDPs when the uncertainty set is specified via either the total variation (TV) distance or $\chi^2$ divergence. The algorithm studied here is a model-based method called {\em distributionally robust value iteration}, which is shown to be near-optimal for the full range of uncertainty levels. Somewhat surprisingly, our results uncover that RMDPs are not necessarily easier or harder to learn than standard MDPs. The statistical consequence incurred by the robustness requirement depends heavily on the size and shape of the uncertainty set: in the case w.r.t.~the TV distance, the minimax sample complexity of RMDPs is always smaller than that of standard MDPs; in the case w.r.t.~the $\chi^2$ divergence, the sample complexity of RMDPs can often far exceed the standard MDP counterpart.

研究强化学习中模型鲁棒性以减少实践中的模拟与实际之间的差距，采用分布鲁棒马尔可夫决策过程的框架，在规定的不确定性集合范围内学习最优性能策略，对于不同的不确定性集合，分别用基于模型的方法分析分布鲁棒价值迭代的采样复杂性，结果表明分布鲁棒马尔可夫决策过程并不一定比标准马尔可夫决策过程更易或更难学习，而是依赖于不确定性集合的大小和形状。

强化学习中生成模型分布稳健性的研究