Scaling Up Robust MDPs by Reinforcement Learning

We consider large-scale Markov decision processes (MDPs) with parameter un-certainty, under the robust MDP paradigm. Previous studies showed that robust MDPs, based on a minimax approach to handle uncertainty, can be solved us-ing dynamic programming for small to medium sized problems. However, due to the “curse of dimensionality”, MDPs that model real-life problems are typically prohibitively large for such approaches. In this work we employ a reinforcement learning approach to tackle this planning problem: we develop a robust approx-imate dynamic programming method based on a projected fixed point equation to approximately solve large scale robust MDPs. We show that the proposed method provably succeeds under certain technical conditions, and demonstrate its effectiveness through simulation of an option pricing problem. To the best of our knowledge, this is the first attempt to scale up the robust MDPs paradigm.