Strongly Polynomial Time Complexity of Policy Iteration for $L_\infty$ Robust MDPs

Abstract:Markov decision processes (MDPs) are a fundamental model in sequential decision making. Robust MDPs (RMDPs) extend this framework by allowing uncertainty in transition probabilities and optimizing against the worst-case realization of that uncertainty. In particular, $(s, a)$-rectangular RMDPs with $L_\infty$ uncertainty sets form a fundamental and expressive model: they subsume classical MDPs and turn-based stochastic games. We consider this model with discounted payoffs. The existence of polynomial and strongly-polynomial time algorithms is a fundamental problem for these optimization models. For MDPs, linear programming yields polynomial-time algorithms for any arbitrary discount factor, and the seminal work of Ye established strongly--polynomial time for a fixed discount factor. The generalization of such results to RMDPs has remained an important open problem. In this work, we show that a robust policy iteration algorithm runs in strongly-polynomial time for $(s, a)$-rectangular $L_\infty$ RMDPs with a constant (fixed) discount factor, resolving an important algorithmic question.

Artificial Intelligence (cs.AI); Computational Complexity (cs.CC)

arXiv:2601.23229 [cs.AI]

(or arXiv:2601.23229v2 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2601.23229 Focus to learn more arXiv-issued DOI via DataCite

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