多臂老虎机的最佳双世界保证改进：具有通用正则化器和多个最优臂的FTRL
Improved Best-of-Both-Worlds Guarantees for Multi-Armed Bandits: FTRL with General Regularizers and Multiple Optimal Arms
AI总结：
本文证明FTRL算法在广泛正则化器族和新学习率调度下无需唯一最优臂假设即可同时实现随机与对抗环境的最优遗憾界，并推广到解耦探索与利用问题。
摘要：
我们研究设计自适应多臂老虎机算法的问题，使其在随机环境和对抗环境中同时实现最优性能（通常称为最佳双世界保证）。近期的一系列工作表明，当配置和分析得当时，原本为对抗环境设计的Follow-the-Regularized-Leader（FTRL）算法实际上也能最优地适应随机环境。然而，这些结果关键依赖于存在唯一最优臂的假设。最近，Ito（2021）迈出了第一步，针对一种使用$\ rac{1}{2}$-Tsallis熵正则化器的特定FTRL算法，移除了这一不理想的唯一性假设。在本工作中，我们显著改进并推广了这一结果，证明对于具有广泛正则化器族和新的学习率调度方案的FTRL，唯一性是不必要的。对于某些正则化器，即使在唯一性成立的情况下，我们的遗憾界也优于先前的结果。我们进一步将我们的结果应用于解耦探索与利用问题，展示了我们的技术具有广泛的适用性。
英文摘要：
We study the problem of designing adaptive multi-armed bandit algorithms that perform optimally in both the stochastic setting and the adversarial setting simultaneously (often known as a best-of-both-world guarantee). A line of recent works shows that when configured and analyzed properly, the Follow-the-Regularized-Leader (FTRL) algorithm, originally designed for the adversarial setting, can in fact optimally adapt to the stochastic setting as well. Such results, however, critically rely on an assumption that there exists one unique optimal arm. Recently, Ito (2021) took the first step to remove such an undesirable uniqueness assumption for one particular FTRL algorithm with the $\frac{1}{2}$-Tsallis entropy regularizer. In this work, we significantly improve and generalize this result, showing that uniqueness is unnecessary for FTRL with a broad family of regularizers and a new learning rate schedule. For some regularizers, our regret bounds also improve upon prior results even when uniqueness holds. We further provide an application of our results to the decoupled exploration and exploitation problem, demonstrating that our techniques are broadly applicable.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
