提出新算法LUCB-H，能自动处理带偏移的离线数据，提升最优选项识别效率。
Best Arm Identification with Possibly Biased Offline Data
- 在标准LUCB框架中引入自适应置信区间与偏差校正机制。
- 当离线数据有帮助时，样本复杂度显著优于传统方法；无偏时性能相当。
- 适用于临床试验等存在数据偏移的实际场景，对偏移未知也具备鲁棒性。
我们研究了在固定置信度设置下，具有可能偏移的离线数据的最佳臂识别（BAI）问题，该问题常见于临床试验等现实场景。证明了在缺乏在线与离线分布间偏差上界先验知识的情况下，自适应算法存在不可能性结果。为此，我们提出LUCB-H算法，通过在LUCB框架中引入辅助偏差校正，实现离线与在线数据的自适应权衡。理论分析表明，当离线数据误导时，LUCB-H的样本复杂度与标准LUCB相当；而当离线数据有益时，显著更优。我们还推导出一个实例相关下界，在某些情况下与LUCB-H的上界匹配。数值实验进一步验证了LUCB-H在有效融合离线数据方面的鲁棒性与自适应能力。
原文摘要 · Abstract (English)
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.
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