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.

翻译：在随机实验中，平衡协变量对于获得可信且高效的实验结果至关重要。重随机化通过反复生成处理分配方案，直至协变量平衡达到预设阈值，以解决此问题。通过缩小该阈值，该方法可实现任意强度的平衡，已有研究结果保证其在多种复杂实验场景下，无论是有限样本还是渐近设定中，均能获得最优估计与有效推断。尽管具有坚实的理论基础，但由于拒绝采样的极端低效性，其实际应用受到限制——在较小阈值下计算速度会变得极其缓慢，这常常迫使实践者采用次优设定，从而导致性能下降。现有聚焦于加速的研究通常无法在可接受分配空间上保持均匀性，因而丧失了经典重随机化的理论依据。基于Metropolis-Hastings框架，我们通过引入一个额外的采样-重要性重采样步骤来应对这一挑战，该步骤恢复了均匀性并保留了统计保证。我们提出的算法PSRSRR在保持精确性与渐近有效性的同时，实现了10至10,000倍的加速效果，这已通过模拟实验和两项实际数据应用得到验证。