改进了多臂赌博机中基于拉伊的置信上界算法，给出了紧致的非渐近误差界。
On Lai's Upper Confidence Bound in Multi-Armed Bandits
- 提出常数探索水平的置信上界索引算法
- 首次获得与拉伊-罗宾斯下界一致的领先常数
- 适用于机器学习中需严格理论保障的决策场景
本文纪念刘志朗（Tze Leung Lai）在多臂赌博机领域的开创性贡献，重点回顾其关于置信上界方法的奠基工作。针对高斯奖励情形，我们为一种具有恒定探索水平的置信上界索引建立了紧致的非渐近后悔界。此外，还为1987年拉伊提出的探索函数随样本量递减的置信上界索引，推导出非渐近后悔界。所有边界中的主导常数均与拉伊-罗宾斯（Lai-Robbins）下界相匹配。研究结果凸显了拉伊早期工作在机器学习文献中应受更多重视的方面。
原文摘要 · Abstract (English)
In this memorial paper, we honor Tze Leung Lai's seminal contributions to the topic of multi-armed bandits, with a specific focus on his pioneering work on the upper confidence bound. We establish sharp non-asymptotic regret bounds for an upper confidence bound index with a constant level of exploration for Gaussian rewards. Furthermore, we establish a non-asymptotic regret bound for the upper confidence bound index of Lai (1987) which employs an exploration function that decreases with the sample size of the corresponding arm. The regret bounds have leading constants that match the Lai-Robbins lower bound. Our results highlight an aspect of Lai's seminal works that deserves more attention in the machine learning literature.
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