Best Arm Identification with Possibly Biased Offline Data

W e 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. W e 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 of-fline 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. W e 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.