Avoiding Model Estimation in Robust Markov Decision Processes with a Generative Model

Robust Markov Decision Processes (MDPs) are getting more attention for learning a robust policy which is less sensitive to environment changes. There are an increasing number of works analyzing sample-efficiency of robust MDPs. However, most works study robust MDPs in a model-based regime, where the transition probability needs to be estimated and requires $\mathcal{O}(|\mathcal{S}|^2|\mathcal{A}|)$ storage in memory. A common way to solve robust MDPs is to formulate them as a distributionally robust optimization (DRO) problem. However, solving a DRO problem is non-trivial, so prior works typically assume a strong oracle to obtain the optimal solution of the DRO problem easily. To remove the need for an oracle, we first transform the original robust MDPs into an alternative form, as the alternative form allows us to use stochastic gradient methods to solve the robust MDPs. Moreover, we prove the alternative form still preserves the role of robustness. With this new formulation, we devise a sample-efficient algorithm to solve the robust MDPs in a model-free regime, from which we benefit lower memory space $\mathcal{O}(|\mathcal{S}||\mathcal{A}|)$ without using the oracle. Finally, we validate our theoretical findings via numerical experiments and show the efficiency to solve the alternative form of robust MDPs.