Rerandomization under Interference

2026-09-27

AI Summary

This study addresses the issue that covariate adjustment under interference may compromise estimation harmlessness and rely on structural assumptions. To overcome this, we propose a restricted rerandomization design that obviates the need to specify the interference structure. By constraining the assignment space, this approach reduces covariate imbalance while permitting covariates to depend on treatment assignments. Furthermore, robust inference is achieved by combining the Hájek estimator with an optimization-based conservative variance estimator. The proposed method attains structure-agnostic precision gains while preserving estimation harmlessness. Theoretically, it is proven to be asymptotically superior to unconstrained Bernoulli randomization, yielding substantial improvements in estimation efficiency.

Abstract

Covariates are widely used in randomized experiments to improve precision. However, in the presence of interference, where outcomes may depend on the treatment assignments of other units, standard covariate adjustment methods may fail to preserve desirable properties such as the no-harm property, meaning that incorporating covariates does not worsen estimator performance. Existing approaches that incorporate covariates under interference typically rely on specifying a particular interference structure, and their guarantees can be sensitive to misspecification. In this paper, we study how to incorporate covariate information in a way that preserves the no-harm property while remaining largely agnostic to the underlying interference structure. We focus on the estimation of the expected average treatment effect (EATE) using the H\'ajek estimator and study rerandomization under interference, a design-stage procedure that restricts the assignment space to allocations with sufficiently small covariate imbalance. Our framework also allows the covariates used for rerandomization to depend on the treatment assignment itself, such as the proportion of treated neighbors, which naturally arises in settings with interference. We show that, even under interference, rerandomization can improve estimation precision asymptotically relative to unrestricted Bernoulli randomization, relying only on mild conditions on the dependence structure across units. When a conservative dependence graph is available, we further develop an optimization-based conservative variance estimator for inference under rerandomization.

Problem

• rerandomization
• interference
• covariate adjustment
• no-harm property
• treatment effect estimation

Innovation

• Rerandomization
• Interference
• Covariate adjustment
• Hájek estimator
• No-harm property