Best Arm Identification with Possibly Biased Offline Data
This addresses a common issue in real-world applications like clinical trials by enabling robust use of offline data, though it is incremental as it builds on the LUCB framework.
The paper tackles the best arm identification problem with potentially biased offline data, proving an impossibility result for adaptive algorithms without bias knowledge and proposing the LUCB-H algorithm that matches standard LUCB sample complexity when data is misleading and significantly outperforms it when helpful.
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.