Efficient Adaptive Experimental Design for Average Treatment Effect Estimation

TL;DR

This work develops an adaptive experimental design to efficiently estimate the average treatment effect (ATE) by minimizing the semiparametric efficiency bound via an efficient treatment-assignment probability, a variant of Neyman allocation. It introduces the Adaptive Augmented Inverse Probability Weighting (A2IPW) estimator, which achieves the bound asymptotically under adaptive treatment assignment, and provides both nonasymptotic and anytime confidence intervals for robust sequential inference. The framework enables rate-optimal sequential hypothesis testing with potential early stopping, supported by finite-sample martingale-based analyses and LIL-based confidence sequences. Empirical results on synthetic and semi-synthetic data demonstrate improved estimation accuracy and competitive or reduced sample sizes compared with traditional RCTs and stratified approaches. The methodology offers a principled, model-flexible path to efficient causal inference in adaptive experimental settings with covariates and sequential data collection.

Abstract

We study how to efficiently estimate average treatment effects (ATEs) using adaptive experiments. In adaptive experiments, experimenters sequentially assign treatments to experimental units while updating treatment assignment probabilities based on past data. We start by defining the efficient treatment-assignment probability, which minimizes the semiparametric efficiency bound for ATE estimation. Our proposed experimental design estimates and uses the efficient treatment-assignment probability to assign treatments. At the end of the proposed design, the experimenter estimates the ATE using a newly proposed Adaptive Augmented Inverse Probability Weighting (A2IPW) estimator. We show that the asymptotic variance of the A2IPW estimator using data from the proposed design achieves the minimized semiparametric efficiency bound. We also analyze the estimator's finite-sample properties and develop nonparametric and nonasymptotic confidence intervals that are valid at any round of the proposed design. These anytime valid confidence intervals allow us to conduct rate-optimal sequential hypothesis testing, allowing for early stopping and reducing necessary sample size.

Figures (2)

• Figure 1: The difference between $K$-fold cross-fitting (left) and adaptive-fitting (right) from Figure 1 in Kato2021adr. The shaded block indicates the subset of observations used for estimating the nuisance parameters.
• Figure 2: Single-stage (left) and sequential (right) hypothesis testing (from Figure 1 in Balsubramani2016).

Theorems & Definitions (36)

• Proposition 1: Semiparametric efficiency bound of ATE estimators. Based on Theorem 1 of Hahn1998.
• Proposition 2: Efficient treatment-assignment probability
• Theorem 1: Asymptotic distribution of the A2IPW estimator
• Corollary 1: Consistency of the A2IPW estimator
• Proposition 3: Asymptotic distribution of the ADR estimator. From Theorem 1 in Kato2021adr.
• Theorem 2: Regret Bound of A2IPW
• Theorem 3: Concentration Inequality of the A2IPW Estimator
• Lemma 1
• Theorem 4: Expected sample size in sequential testing
• Corollary 2