Policy Gradient Algorithms for Robust MDP\(s\) with Nonrectangular Uncertainty Sets

This is the authors' abstract. We don't add key points for this paper.

We propose policy gradient algorithms for robust infinite-horizon Markov decision processes (MDPs) with nonrectangular uncertainty sets, thereby addressing an open challenge in the robust MDP literature. Indeed, uncertainty sets that display statistical optimality properties and make optimal use of limited data often fail to be rectangular. Unfortunately, the corresponding robust MDPs cannot be solved with dynamic programming techniques and are in fact provably intractable. We first present a randomized projected Langevin dynamics algorithm that solves the robust policy evaluation problem to global optimality but is inefficient. We also propose a deterministic policy gradient method that is efficient but solves the robust policy evaluation problem only approximately, and we prove that the approximation error scales with a new measure of nonrectangularity of the uncertainty set. Finally, we describe an actor-critic algorithm that finds an [Formula: see text]-optimal solution for the robust policy improvement problem in [Formula: see text] iterations. We thus present the first complete solution scheme for robust MDPs with nonrectangular uncertainty sets offering global optimality guarantees. Numerical experiments show that our algorithms compare favorably against state-of-the-art methods.