（Ting Li  & Chengchun Shi & Qianglin Wen & Yang Sui & Yongli Qin &  Chunbo Lai & Hongtu Zhu ）

摘要：This paper studied policy evaluation with multiple data sources, especially in scenarios that involve one experimental dataset with two arms, complemented by a historical dataset generated under a single control arm. They proposed novel data integration methods that linearly integrate base policy value estimators constructed based on the experimental and historical data, with weights optimized to minimize the mean square error (MSE) of the resulting combined estimator. They further applied the pessimistic principle to obtain more robust estimators, and extended these developments to sequential decision making. Theoretically, they established non-asymptotic error bounds for the MSEs of our proposed estimators, and derive their oracle, efficiency and robustness properties across a broad spectrum of reward shift scenarios. Numerical experiments and real-data-based analyses from a ridesharing company demonstrated the superior performance of the proposed estimators.