This paper formulates a new Best-Arm Identification problem in the non-stationary stochastic bandits setting, where the means of all arms are shifted in the same way due to a global influence of the environment. The aim is to identify the unique best arm across environmental change given a fixed total budget. While this setting can be regarded as a special case of Adversarial Bandits or Corrupted Bandits, we demonstrate that existing solutions tailored to those settings do not fully utilise the nature of this global influence, and thus, do not work well in practice (despite their theoretical guarantees). To overcome this issue, in this paper we develop a novel selection policy that is consistent and robust in dealing with global environmental shifts. We then propose an allocation policy, LinLUCB, which exploits information about global shifts across all arms in each environment. Empirical tests depict a significant improvement in our policies against other existing methods.

翻译：本文在非平稳随机多臂赌博机框架下，提出了一种新的最优臂识别问题，其中所有臂的期望收益会因环境的全局性影响而发生同向偏移。研究目标是在给定固定总预算的条件下，识别出跨越环境变迁的全局最优臂。虽然该设定可视为对抗性赌博机或污染赌博机的特例，但我们证明针对这些场景设计的现有解决方案未能充分利用全局影响的本质特性，因而在实际应用中表现欠佳（尽管其理论保证成立）。为解决该问题，本文提出了一种在处理全局环境变迁时具有一致性与鲁棒性的新颖选择策略。进而设计出分配策略LinLUCB，该策略能充分挖掘每个环境中所有臂的全局偏移信息。实证测试表明，相较于现有方法，本文提出的策略取得了显著性能提升。