Budgeted Active Experimentation for Treatment Effect Estimation from Observational and Randomized Data

Estimating heterogeneous treatment effects is central to data-driven decision-making, yet industrial applications often face a fundamental tension between limited randomized controlled trial (RCT) budgets and abundant but biased observational data (OBS) collected under historical targeting policies. Although observational logs offer the advantage of scale, they may suffer from severe policy-induced imbalance and overlap violations, rendering standalone estimation unreliable. We propose a budgeted active experimentation framework that iteratively collects informative randomized samples for causal effect estimation via active sampling. By leveraging observational signals, we develop an acquisition function targeting uplift estimation uncertainty, domain discrepancy, and overlap deficits to select the most informative units for randomized experiments. We establish finite-sample deviation bounds, asymptotic normality via martingale CLTs, and minimax lower bounds showing near-optimality in the linear representation setting. Experiments on synthetic datasets support our theoretical findings, and further extensions to industrial neural network-based uplift modeling scenarios show that active sampling can improve sample efficiency over random sampling under limited RCT budgets.