标题： 最优臂识别与可能存在偏倚的离线数据 显示英文标题

标题： Best Arm Identification with Possibly Biased Offline Data

摘要： 我们研究了固定置信度设置下具有潜在偏倚离线数据的最佳臂识别（BAI）问题，此类问题在现实世界场景中很常见，例如临床试验。 我们证明了在没有关于在线和离线分布之间偏倚界值的先验知识的情况下，自适应算法不可能实现。 为了解决这个问题，我们提出了LUCB-H算法，该算法通过引入辅助偏差校正来整合自适应置信边界，在LUCB框架内平衡离线和在线数据。 理论分析表明，当离线数据具有误导性时，LUCB-H的样本复杂度与标准LUCB相当；而当离线数据有帮助时，其表现显著优于标准LUCB。 我们还推导出一种实例相关的下界，该下界在某些情况下与LUCB-H的上界相匹配。 数值实验进一步展示了LUCB-H在有效结合离线数据方面的鲁棒性和适应性。 显示英文摘要

摘要： We study the best arm identification (BAI) problem with potentially biased offline data in the fixed confidence setting, which commonly arises in real-world scenarios such as clinical trials. We prove an impossibility result for adaptive algorithms without prior knowledge of the bias bound between online and offline distributions. To address this, we propose the LUCB-H algorithm, which introduces adaptive confidence bounds by incorporating an auxiliary bias correction to balance offline and online data within the LUCB framework. Theoretical analysis shows that LUCB-H matches the sample complexity of standard LUCB when offline data is misleading and significantly outperforms it when offline data is helpful. We also derive an instance-dependent lower bound that matches the upper bound of LUCB-H in certain scenarios. Numerical experiments further demonstrate the robustness and adaptability of LUCB-H in effectively incorporating offline data.