Achieving an $O(1/N)$ Optimality Gap in Average-Reward Weakly-Coupled MDPs

Abstract:We study average-reward weakly-coupled Markov decision processes (WCMDPs), where a WCMDP consists of $N$ smaller MDPs, called arms, that share multiple per-step budget constraints. We consider the setting where the arms have identical model parameters, multiple actions, and state- and action-dependent costs. For restless bandits (RBs), a well-studied special case of WCMDPs, prior work has developed policies that achieve an $O(1/\sqrt{N})$ optimality gap under general conditions, and has further identified conditions under which policies can achieve a better-than-$1/\sqrt{N}$ optimality gap. However, for general WCMDPs, no prior result achieves an optimality gap better than $1/\sqrt{N}$. In this paper, we identify conditions analogous to those for RBs under which a better-than-$1/\sqrt{N}$ optimality gap is achievable, and design a policy that attains an $O(1/N)$ optimality gap. Notably, unlike prior approaches based on generalizing priority orderings, our policy is not priority-based but rather is designed to induce locally linear mean-field dynamics.

Machine Learning (cs.LG); Optimization and Control (math.OC); Probability (math.PR)

arXiv:2609.38132 [cs.LG]

(or arXiv:2609.38132v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.38132 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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