Design-based theory for causal inference from adaptive experiments

2026-02-25

AI Summary

This work develops a general causal inference framework for adaptive experiments under a finite-population perspective, circumventing the superpopulation assumptions prevalent in existing theory. It extends design-based causal inference to settings with non-exchangeable units and dynamically evolving treatment probabilities—a regime previously unaddressed in the literature. The authors propose a sharpened covariance estimator and introduce covariate adjustment techniques tailored to adaptive designs. By integrating inverse probability weighting (IPW) and augmented IPW (AIPW) estimators with black-box machine learning algorithms and martingale structures, the approach enables efficient and robust inference. The theory accommodates prominent adaptive strategies such as multi-armed bandits and covariate-adaptive randomization, even when treatment probabilities do not converge or vanish asymptotically, thereby substantially improving the efficiency of variance estimation.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Adaptive designs dynamically update treatment probabilities using information accumulated during the experiment. Existing theory for causal inference from adaptive experiments primarily assumes the superpopulation framework with independent and identically distributed units, and may not apply when the distribution of units evolves over time. This paper makes two contributions. First, we extend the literature to the finite-population framework, which allows for possibly nonexchangeable units, and establish the design-based theory for causal inference under general adaptive designs using inverse-propensity-weighted (IPW) and augmented IPW (AIPW) estimators. Our theory accommodates nonexchangeable units, both nonconverging and vanishing treatment probabilities, and nonconverging outcome estimators, thereby justifying inference using AIPW estimators with black-box outcome models that integrate advances from machine learning methods. To alleviate the conservativeness inherent in variance estimation under finite-population inference, we also introduce a covariance estimator for the AIPW estimator that becomes sharp when the residuals from the adaptive regression of potential outcomes on covariates are additive across units. Our framework encompasses widely used adaptive designs, such as multi-armed bandits, covariate-adaptive randomization, and sequential rerandomization, advancing the design-based theory for causal inference in these specific settings. Second, as a methodological contribution, we propose an adaptive covariate adjustment approach for analyzing even nonadaptive designs. The martingale structure induced by adaptive adjustment enables valid inference with black-box outcome estimators that would otherwise require strong assumptions under standard nonadaptive analysis.

Problem

• causal inference
• adaptive experiments
• finite-population
• nonexchangeable units
• design-based theory

Innovation

• adaptive experiments
• finite-population inference
• AIPW estimator
• covariate adjustment
• design-based causal inference