Optimistic Algorithms for Adaptive Estimation of the Average Treatment Effect

2025-02-07

AI Summary

This paper addresses the exploration-exploitation imbalance and suboptimality of existing estimators for average treatment effect (ATE) estimation under limited sample sizes. We propose an online sequential causal inference framework grounded in the augmented inverse probability weighting (AIPW) optimal estimator. Methodologically, we pioneer the integration of optimistic sampling—inspired by multi-armed bandits—into adaptive sequential experimental design, coupled with martingale-theoretic guarantees to ensure finite-sample statistical reliability. Theoretically, we break beyond asymptotic analysis by establishing the first finite-sample convergence and efficiency guarantees for adaptive ATE estimation. Empirically, our approach significantly improves ATE estimation accuracy and inferential robustness on both synthetic and real-world datasets, achieving superior statistical efficiency over state-of-the-art baselines.

Technology Category

• Machine Learning: Online Learning & Bandits
• Reasoning under Uncertainty: Sequential Decision Making
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising

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.

Problem

• Adaptive estimation of ATE
• Exploration-exploitation tradeoffs
• Optimistic algorithmic design principle

Innovation

• Adaptive sampling with AIPW
• Optimism-inspired algorithmic design
• Enhancing finite-sample causal inference