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arXiv · 2502.06072

Projection-based Lyapunov method for fully heterogeneous weakly-coupled MDPs

Xiangcheng Zhang·Yige Hong·Weina Wang
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Abstract

Heterogeneity poses a fundamental challenge for many real-world large-scale decision-making problems but remains largely understudied. In this paper, we study the fully heterogeneous setting of a prominent class of such problems, known as weakly-coupled Markov decision processes (WCMDPs). Each WCMDP consists of $N$ arms (or subproblems), which have distinct model parameters in the fully heterogeneous setting, leading to the curse of dimensionality when $N$ is large. We show that, under mild assumptions, an efficiently computable policy achieves an $O(1/\sqrt{N})$ optimality gap in the long-run average reward per arm for fully heterogeneous WCMDPs as $N$ becomes large. This is the first asymptotic optimality result for fully heterogeneous average-reward WCMDPs. Our main technical innovation is the construction of projection-based Lyapunov functions that certify the convergence of rewards and costs to an optimal region, even under full heterogeneity.

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Xiangcheng Zhang, Yige Hong, Weina Wang. 2025-02-09. Projection-based Lyapunov method for fully heterogeneous weakly-coupled MDPs. https://arxiv.org/abs/2502.06072

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