Efficient Algorithms for Robust Markov Decision Processes with $s$-Rectangular Ambiguity Sets

• URL: http://arxiv.org/abs/2602.05591v1
• Date: Thu, 05 Feb 2026 12:20:26 GMT
• Title: Efficient Algorithms for Robust Markov Decision Processes with $s$-Rectangular Ambiguity Sets
• Authors: Chin Pang Ho, Marek Petrik, Wolfram Wiesemann,
• Abstract summary: We develop a unified solution framework for a class of robust MDPs with $s$-rectangular ambiguity sets.<n>Using our algorithms, we show that $s$-rectangular robust MDPs with $1$- and $2$-norm as well as $$-divergence ambiguity sets can be solved several orders of magnitude faster than with state-of-the-art commercial solvers.
• Score: 19.053062263045664
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Robust Markov decision processes (MDPs) have attracted significant interest due to their ability to protect MDPs from poor out-of-sample performance in the presence of ambiguity. In contrast to classical MDPs, which account for stochasticity by modeling the dynamics through a stochastic process with a known transition kernel, a robust MDP additionally accounts for ambiguity by optimizing against the most adverse transition kernel from an ambiguity set constructed via historical data. In this paper, we develop a unified solution framework for a broad class of robust MDPs with $s$-rectangular ambiguity sets, where the most adverse transition probabilities are considered independently for each state. Using our algorithms, we show that $s$-rectangular robust MDPs with $1$- and $2$-norm as well as $φ$-divergence ambiguity sets can be solved several orders of magnitude faster than with state-of-the-art commercial solvers, and often only a logarithmic factor slower than classical MDPs. We demonstrate the favorable scaling properties of our algorithms on a range of synthetically generated as well as standard benchmark instances.

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