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In high-stake scenarios like medical treatment and auto-piloting, it's riskyor even infeasible to collect online experimental data to train the agent.Simulation-based training can alleviate this issue, but may suffer from itsinherent mismatches from the simulator and real environment. It is thereforeimperative to utilize the simulator to learn a robust policy for the real-worlddeployment. In this work, we consider policy learning for Robust MarkovDecision Processes (RMDP), where the agent tries to seek a robust policy withrespect to unexpected perturbations on the environments. Specifically, we focuson the setting where the training environment can be characterized as agenerative model and a constrained perturbation can be added to the modelduring testing. Our goal is to identify a near-optimal robust policy for theperturbed testing environment, which introduces additional technicaldifficulties as we need to simultaneously estimate the training environmentuncertainty from samples and find the worst-case perturbation for testing. Tosolve this issue, we propose a generic method which formalizes the perturbationas an opponent to obtain a two-player zero-sum game, and further show that theNash Equilibrium corresponds to the robust policy. We prove that, with apolynomial number of samples from the generative model, our algorithm can finda near-optimal robust policy with a high probability. Our method is able todeal with general perturbations under some mild assumptions and can also beextended to more complex problems like robust partial observable Markovdecision process, thanks to the game-theoretical formulation.

Policy Learning for Robust Markov Decision Process with a Mismatched Generative Model