Fast Rerandomization for Balancing Covariates in Randomized Experiments: A Metropolis-Hastings Framework

2026-02-07

AI Summary

Traditional rerandomization becomes computationally impractical under stringent covariate balance constraints due to the inefficiency of rejection sampling, particularly when tight thresholds are imposed. This work proposes PSRSRR, an accelerated algorithm grounded in the Metropolis–Hastings framework, which incorporates a sampling–importance resampling (SIR) step to efficiently generate uniformly distributed treatment assignments under prespecified balance conditions. PSRSRR is the first method to substantially enhance computational efficiency while rigorously preserving uniformity over the admissible randomization space, thereby maintaining the statistical validity and theoretical guarantees of classical rerandomization. Empirical evaluations on both simulated and real-world datasets demonstrate speedups ranging from 10 to 10,000 times, with reliable performance in both finite-sample and asymptotic inference settings.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Balancing covariates is critical for credible and efficient randomized experiments. Rerandomization addresses this by repeatedly generating treatment assignments until covariate balance meets a prespecified threshold. By shrinking this threshold, it can achieve arbitrarily strong balance, with established results guaranteeing optimal estimation and valid inference in both finite-sample and asymptotic settings across diverse complex experimental settings. Despite its rigorous theoretical foundations, practical use is limited by the extreme inefficiency of rejection sampling, which becomes prohibitively slow under small thresholds and often forces practitioners to adopt suboptimal settings, leading to degraded performance. Existing work focusing on acceleration typically fail to maintain the uniformity over the acceptable assignment space, thus losing the theoretical grounds of classical rerandomization. Building upon a Metropolis-Hastings framework, we address this challenge by introducing an additional sampling-importance resampling step, which restores uniformity and preserves statistical guarantees. Our proposed algorithm, PSRSRR, achieves speedups ranging from 10 to 10,000 times while maintaining exact and asymptotic validity, as demonstrated by simulations and two real-data applications.

Problem

• rerandomization
• covariate balance
• Metropolis-Hastings
• uniform sampling
• randomized experiments

Innovation

• Rerandomization
• Metropolis-Hastings
• Covariate balance
• Sampling-importance resampling
• Randomized experiments