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 i.i.d. 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.

翻译：模拟退火（ST）是一种用于复杂目标分布的MCMC算法，通过目标分布与更易处理的参考分布之间的路径进行采样。关键在于，当参考分布支持独立同分布采样时，ST具有再生性，并且可以在独立遍历过程中进行并行化。然而，ST调参的困难阻碍了其广泛应用。本文提出了一种简单的不可逆ST（NRST）算法、一套通用的ST理论分析框架以及ST的自动调参程序。理论分析的核心贡献在于提出了一种新型性能指标——遍历有效性（TE），该指标可控制有界测试函数下ST估计量的渐近方差。我们利用TE证明了NRST优于其可逆对应方法，进而开发了针对NRST算法的自动调参程序，该程序在最小化计算成本的同时优化TE。这一程序使NRST能够轻松集成到现有的概率编程语言中。我们通过大量实验证明，所提出的调参方案在多种概率模型上显著提升了NRST算法的性能与鲁棒性。