Scalable First-Order Methods for Robust MDPs

• URL: http://arxiv.org/abs/2005.05434v5
• Date: Thu, 14 Jan 2021 21:06:53 GMT
• Title: Scalable First-Order Methods for Robust MDPs
• Authors: Julien Grand-Cl\'ement, Christian Kroer
• Abstract summary: This paper proposes the first first-order framework for solving robust MDPs. By carefully controlling the tradeoff between the accuracy and cost of Value Iteration updates, we achieve an ergodic convergence rate of $O left( A2 S3log(S)log(epsilon-1) epsilon-1 right)$
• Score: 31.29341288414507
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Robust Markov Decision Processes (MDPs) are a powerful framework for modeling sequential decision-making problems with model uncertainty. This paper proposes the first first-order framework for solving robust MDPs. Our algorithm interleaves primal-dual first-order updates with approximate Value Iteration updates. By carefully controlling the tradeoff between the accuracy and cost of Value Iteration updates, we achieve an ergodic convergence rate of $O \left( A^{2} S^{3}\log(S)\log(\epsilon^{-1}) \epsilon^{-1} \right)$ for the best choice of parameters on ellipsoidal and Kullback-Leibler $s$-rectangular uncertainty sets, where $S$ and $A$ is the number of states and actions, respectively. Our dependence on the number of states and actions is significantly better (by a factor of $O(A^{1.5}S^{1.5})$) than that of pure Value Iteration algorithms. In numerical experiments on ellipsoidal uncertainty sets we show that our algorithm is significantly more scalable than state-of-the-art approaches. Our framework is also the first one to solve robust MDPs with $s$-rectangular KL uncertainty sets.

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