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arXiv Machine Learning By Han Zhong, Yinyu Ye

Linear Programming Representations and Strongly Polynomial Algorithms for Robust Markov Decision Processes

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The paper presents linear programming formulations and strongly polynomial algorithms for robust Markov decision processes (RMDPs) with rational polyhedral state-action rectangular uncertainty in rewards and transitions. By encoding a finite sequence of robust policy-iteration steps, a single LP is constructed whose optimal solutions recover the robust optimal value and all optimal stationary randomized policies. The authors provide a general complexity analysis of robust policy iteration, improving known bounds for α1 and α1∞ RMDPs and establishing new strongly polynomial bounds for general interval, weighted α1, and Wasserstein RMDPs, as well as turn‑based stochastic games with these uncertainty sets.

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