Restless Bandits with Average Reward: Breaking the Uniform Global Attractor Assumption

• URL: http://arxiv.org/abs/2306.00196v3
• Date: Tue, 16 Jan 2024 05:42:06 GMT
• Title: Restless Bandits with Average Reward: Breaking the Uniform Global Attractor Assumption
• Authors: Yige Hong, Qiaomin Xie, Yudong Chen, Weina Wang
• Abstract summary: A fundamental goal is to efficiently compute policies that achieve a diminishing optimality gap as the number of arms, $N$, grows large. Existing results on optimality all rely on the uniform global attractor property (UGAP), a complex and challenging-to-verify assumption. We propose a general, simulation-based framework, that converts any single-armed policy into a policy for the original $N$-armed problem.
• Score: 12.471848976031904
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the infinite-horizon restless bandit problem with the average reward criterion, in both discrete-time and continuous-time settings. A fundamental goal is to efficiently compute policies that achieve a diminishing optimality gap as the number of arms, $N$, grows large. Existing results on asymptotic optimality all rely on the uniform global attractor property (UGAP), a complex and challenging-to-verify assumption. In this paper, we propose a general, simulation-based framework, Follow-the-Virtual-Advice, that converts any single-armed policy into a policy for the original $N$-armed problem. This is done by simulating the single-armed policy on each arm and carefully steering the real state towards the simulated state. Our framework can be instantiated to produce a policy with an $O(1/\sqrt{N})$ optimality gap. In the discrete-time setting, our result holds under a simpler synchronization assumption, which covers some problem instances that violate UGAP. More notably, in the continuous-time setting, we do not require \emph{any} additional assumptions beyond the standard unichain condition. In both settings, our work is the first asymptotic optimality result that does not require UGAP.

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