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

Fuente: arXiv
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Main Authors: Ho, Chin Pang, Petrik, Marek, Wiesemann, Wolfram
Format: Preprint
Published: 2026
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author Ho, Chin Pang
Petrik, Marek
Wiesemann, Wolfram
author_facet Ho, Chin Pang
Petrik, Marek
Wiesemann, Wolfram
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2602_05591
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Efficient Algorithms for Robust Markov Decision Processes with $s$-Rectangular Ambiguity Sets
Ho, Chin Pang
Petrik, Marek
Wiesemann, Wolfram
Optimization and Control
Machine Learning
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.
title Efficient Algorithms for Robust Markov Decision Processes with $s$-Rectangular Ambiguity Sets
topic Optimization and Control
Machine Learning
url https://arxiv.org/abs/2602.05591