Automatic Regenerative Simulation via Non-Reversible Simulated Tempering

Simulated Tempering (ST) is an MCMC algorithm for complex target distributions that operates on a path between the target and a more amenable reference distribution. Crucially, if the reference enables iid sampling, ST is regenerative and can be parallelized across independent tours. However, the difficulty of tuning ST has hindered its widespread adoption. In this work, we develop a simple nonreversible ST (NRST) algorithm, a general theoretical analysis of ST, and an automated tuning procedure for ST. A core contribution that arises from the analysis is a novel performance metric—Tour Effectiveness (TE)—that controls the asymptotic variance of estimates from ST for bounded test functions. We use the TE to show that NRST dominates its reversible counterpart. We then develop an automated tuning procedure for NRST algorithms that targets the TE while minimizing computational cost. This procedure enables straightforward integration of NRST into existing probabilistic programming languages. We provide extensive experimental evidence that our tuning scheme improves the performance and robustness of NRST algorithms on a diverse set of probabilistic models. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.模拟回火（Simulated Tempering, ST）是一种针对复杂目标分布的马尔可夫链蒙特卡洛（Markov Chain Monte Carlo, MCMC）算法，其运行于目标分布与更易处理的参考分布之间的路径上。核心特性在于，若参考分布支持独立同分布（independent and identically distributed, iid）采样，则ST具备再生性，且可跨独立遍历实现并行化。然而，ST的调参难题阻碍了其广泛应用。本研究提出了一种简单的不可逆模拟回火（Nonreversible Simulated Tempering, NRST）算法，完成了针对ST的一般性理论分析，并开发了适用于ST的自动化调参流程。本分析得出的核心贡献之一，是提出了一种全新的性能指标——遍历有效性（Tour Effectiveness, TE），该指标可控制有界检验函数下ST估计量的渐近方差。借助该指标，我们证明了NRST的性能优于其可逆版本。随后，我们开发了针对NRST算法的自动化调参流程，该流程以遍历有效性为优化目标，同时最小化计算开销。此流程可便捷地将NRST集成至现有概率编程语言（probabilistic programming languages）中。我们提供了大量实验证据，表明所提调参方案可提升NRST算法在多样概率模型集合上的性能与鲁棒性。本文的补充材料可在线获取，其中包含了用于复现本研究的标准化材料说明。