Robust Phi-Divergence MDPs

• URL: http://arxiv.org/abs/2205.14202v1
• Date: Fri, 27 May 2022 19:08:55 GMT
• Title: Robust Phi-Divergence MDPs
• Authors: Chin Pang Ho, Marek Petrik, Wolfram Wiesemann
• Abstract summary: We develop a novel solution framework for robust MDPs with s-rectangular ambiguity sets. We show that the associated s-rectangular robust MDPs can be solved substantially faster than with state-of-the-art commercial solvers.
• Score: 13.555107578858307
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In recent years, robust Markov decision processes (MDPs) have emerged as a prominent modeling framework for dynamic decision problems affected by uncertainty. In contrast to classical MDPs, which only account for stochasticity by modeling the dynamics through a stochastic process with a known transition kernel, robust MDPs additionally account for ambiguity by optimizing in view of the most adverse transition kernel from a prescribed ambiguity set. In this paper, we develop a novel solution framework for robust MDPs with s-rectangular ambiguity sets that decomposes the problem into a sequence of robust Bellman updates and simplex projections. Exploiting the rich structure present in the simplex projections corresponding to phi-divergence ambiguity sets, we show that the associated s-rectangular robust MDPs can be solved substantially faster than with state-of-the-art commercial solvers as well as a recent first-order solution scheme, thus rendering them attractive alternatives to classical MDPs in practical applications.

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