Optimistic Algorithms for Adaptive Estimation of the Average Treatment Effect

TL;DR

This paper introduces an optimistic adaptive sampling algorithm for estimating the Average Treatment Effect, leveraging martingale theory and AIPW estimators to improve finite-sample inference in causal studies.

Contribution

It develops a novel adaptive sampling algorithm based on optimism principles that outperforms existing methods in finite-sample causal inference settings.

Findings

Achieves significant theoretical improvements over prior methods.

Demonstrates empirical gains in estimation accuracy.

Addresses challenges overlooked by asymptotic analyses.

Abstract

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 tradeoffs 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 multiarmed bandits. This principled approach enables our algorithm to achieve significant theoretical and empirical gains compared to prior methods. Our findings mark a step forward in advancing adaptive causal inference methods in theory and practice.