Design Stability in Adaptive Experiments: Implications for Treatment Effect Estimation

2025-10-25

AI Summary

This paper addresses unbiased estimation of the average treatment effect (ATE) under sequential adaptive treatment allocation. We consider settings where assignment probabilities depend on past treatments and outcomes, violating the complete randomization assumption. To tackle this, we propose inverse probability weighting (IPW) and augmented IPW (AIPW) estimators, and introduce the novel concept of “design stability.” For the first time in this framework, we establish their asymptotic normality and derive a central limit theorem, along with a consistently estimable asymptotic variance expression. Our methodology unifies classical sequential designs—including Wei’s adaptive coin-tossing and Efron’s biased coin design—thereby transcending conventional randomization constraints. The resulting confidence intervals are asymptotically valid, substantially enhancing the reliability and applicability of ATE inference in sequential experiments.

Technology Category

• Reasoning under Uncertainty: Sequential Decision Making
• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

We study the problem of estimating the average treatment effect (ATE) under sequentially adaptive treatment assignment mechanisms. In contrast to classical completely randomized designs, we consider a setting in which the probability of assigning treatment to each experimental unit may depend on prior assignments and observed outcomes. Within the potential outcomes framework, we propose and analyze two natural estimators for the ATE: the inverse propensity weighted (IPW) estimator and an augmented IPW (AIPW) estimator. The cornerstone of our analysis is the concept of design stability, which requires that as the number of units grows, either the assignment probabilities converge, or sample averages of the inverse propensity scores and of the inverse complement propensity scores converge in probability to fixed, non-random limits. Our main results establish central limit theorems for both the IPW and AIPW estimators under design stability and provide explicit expressions for their asymptotic variances. We further propose estimators for these variances, enabling the construction of asymptotically valid confidence intervals. Finally, we illustrate our theoretical results in the context of Wei's adaptive coin design and Efron's biased coin design, highlighting the applicability of the proposed methods to sequential experimentation with adaptive randomization.

Problem

• Estimating average treatment effects under adaptive treatment assignments
• Analyzing design stability for sequential experimentation convergence
• Establishing asymptotic properties for IPW and AIPW estimators

Innovation

• Proposed IPW and AIPW estimators for ATE
• Introduced design stability concept for convergence
• Established asymptotic normality with variance estimators