Summary of Achieving Exponential Asymptotic Optimality in Average-reward Restless Bandits Without Global Attractor Assumption, by Yige Hong et al.
Achieving Exponential Asymptotic Optimality in Average-Reward Restless Bandits without Global Attractor Assumption
by Yige Hong, Qiaomin Xie, Yudong Chen, Weina Wang
First submitted to arxiv on: 28 May 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Optimization and Control (math.OC); Probability (math.PR)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The infinite-horizon average-reward restless bandit problem is tackled using a novel two-set policy approach. This method maintains two dynamic subsets of arms: one subset with nearly optimal state distribution, controlled by an Optimal Local Control routine, and another subset driven towards the optimal state distribution and gradually merged into the first subset. The two-set policy is shown to be asymptotically optimal with an O(exp(-C N)) optimality gap for an N-armed problem under mild assumptions of aperiodic-unichain, non-degeneracy, and local stability. This policy achieves exponential asymptotic optimality under these assumptions, whereas prior work either required a strong global attractor assumption or achieved only an O(1/√N) optimality gap. The authors also discuss obstacles in weakening the assumptions by demonstrating examples where exponential asymptotic optimality is not achievable when any of the three assumptions is violated. A lower bound is proved for a large class of locally unstable restless bandits, highlighting the importance of local stability for exponential asymptotic optimality. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper looks at a problem called the infinite-horizon average-reward restless bandit problem. They come up with a new way to solve it using a “two-set policy”. This means they divide the options into two groups: one that is already doing well and another that needs help getting better. They show that this approach works really well and is even better than previous methods in some cases. |
