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

arXiv: https://arxiv.org/abs/2602.07613 · HTML: https://mlsanity.com/paper/2602.07613/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 63 references that are in the map.
- First posted on arXiv 7 Feb 2026.

## Builds on (most cited first, 18 of 18)

- [Balancing Covariates in Randomized Experiments with the Gram-Schmidt Walk Design](https://mlsanity.com/paper/1911.03071/) (2019)
- [A Scalable and Nearly Uniform Generator of SAT Witnesses](https://mlsanity.com/paper/1304.1584/) (2013)
- [Model-assisted design of experiments in the presence of network correlated outcomes](https://mlsanity.com/paper/1507.00803/) (2015)
- [Challenges in Statistics: A Dozen Challenges in Causality and Causal Inference](https://mlsanity.com/paper/2508.17099/) (2025)
- [On Efficient Estimation of Distributional Treatment Effects under Covariate-Adaptive Randomization](https://mlsanity.com/paper/2506.05945/) (2025)
- [Randomization Tests for Weak Null Hypotheses in Randomized Experiments](https://mlsanity.com/paper/1809.07419/) (2018)
- [Independent-Set Design of Experiments for Estimating Treatment and Spillover Effects under Network Interference](https://mlsanity.com/paper/2312.04026/) (2023)
- [Leveraging the Fisher randomization test using confidence distributions: inference, combination and fusion learning](https://mlsanity.com/paper/2004.08472/) (2020)
- [Covariate-adjusted Fisher randomization tests for the average treatment effect](https://mlsanity.com/paper/2010.14555/) (2020)
- [Randomization Inference beyond the Sharp Null: Bounded Null Hypotheses and Quantiles of Individual Treatment Effects](https://mlsanity.com/paper/2101.09195/) (2021)
- [Rerandomization with Diminishing Covariate Imbalance and Diverging Number of Covariates](https://mlsanity.com/paper/2109.02578/) (2021)
- [Rejective Sampling, Rerandomization and Regression Adjustment in Survey Experiments](https://mlsanity.com/paper/2109.09930/) (2021)
- [Rerandomization in 2K Factorial Experiments](https://mlsanity.com/paper/1812.10911/) (2018)
- [Gaussian Prepivoting for Finite Population Causal Inference](https://mlsanity.com/paper/2002.06654/) (2020)
- [No star is good news: A unified look at rerandomization based on p-values from covariate balance tests](https://mlsanity.com/paper/2112.10545/) (2021)
- [Design-based theory for cluster rerandomization](https://mlsanity.com/paper/2207.02540/) (2022)
- [A Unified Framework for Rerandomization using Quadratic Forms](https://mlsanity.com/paper/2403.12815/) (2024)
- [Asymptotic inference with flexible covariate adjustment under rerandomization and stratified rerandomization](https://mlsanity.com/paper/2406.02834/) (2024)

## Abstract (arXiv)

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.