Strongly Polynomial Time Complexity of Policy Iteration for L_infty Robust MDPs

arXiv:2601.23229v2 Announce Type: replace 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.

Source: arXiv cs.AI | 2026-06-03