Optimistic Algorithms for Adaptive Estimation of the Average Treatment Effect

Estimation and inference for the Average Treatment Effect (ATE) is a cornerstone of causal inference and often serves as the foundation for developing procedures for more complicated settings. Although traditionally analyzed in a batch setting, recent advances in martingale theory have paved the way for adaptive methods that can enhance the power of downstream inference. Despite these advances, progress in understanding and developing adaptive algorithms remains in its early stages. Existing work either focus on asymptotic analyses that overlook exploration-exploitation trade-offs relevant in finite-sample regimes or rely on simpler but suboptimal estimators.In this work, we address these limitations by studying adaptive sampling procedures that take advantage of the asymptotically optimal Augmented Inverse Probability Weighting (AIPW) estimator. Our analysis uncovers challenges obscured by asymptotic approaches and introduces a novel algorithmic design principle reminiscent of optimism in multi-armed bandits. This principled approach enables our algorithm to achieve significant theoretical and empirical gains compared to previous methods. Our findings mark a step forward in the advancement of adaptive causal inference methods in theory and practice.

Randomized controlled trials determine whether new treatments—such as drugs or educational programs—work better than existing approaches. These trials are expensive and time-consuming, requiring many participants to reach reliable conclusions. We developed a method that uses information from early trial participants to intelligently select future participants, potentially cutting the required sample size significantly. While previous research addressed this challenge assuming unlimited participants, real clinical trials often work with small groups where every participant counts. Our approach specifically targets these small-sample scenarios. The key insight is that the algorithm must be "optimistic"—actively testing groups where it suspects larger treatment differences might exist, rather than playing it safe. This strategic optimism allows the trial to focus resources where they matter most. In practical terms, this could mean reaching the same conclusions with half the participants, reducing both costs and the time needed to bring effective treatments to patients.