Pessimistic Data Integration for Policy Evaluation
Xiangkun Wu, Ting Li, Gholamali Aminian, Armin Behnamnia, Hamid Rabiee, Chengchun Shi
This paper studies how to integrate historical control data with experimental data to enhance A/B testing, while addressing the distributional shift between historical and experimental datasets. We propose a pessimistic data integration method that combines two causal effect estimators constructed based on experimental and historical datasets. Our main idea is to conceptualize the weight function for this combination as a policy so that existing pessimistic policy learning algorithms are applicable to learn the optimal weight that minimizes the resulting weighted  estimator's mean squared error. Additionally, we conduct comprehensive theoretical and empirical analyses to compare our method against various baseline estimators across five scenarios. Both our theoretical and numerical findings demonstrate that the proposed estimator achieves near-optimal performance across all scenarios.