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）是一种针对复杂目标分布的马尔可夫链蒙特卡洛（MCMC）算法，通过在目标分布与更易处理的参考分布之间构建路径来运行。关键在于，若参考分布支持独立同分布采样，则ST具有回归性，并可跨独立游程并行化。然而，ST的参数调优困难阻碍了其广泛采用。本文提出一种简单的不可逆ST（NRST）算法，构建了ST的通用理论分析框架，并开发了ST的自动化调优流程。分析中的核心贡献在于提出了一种全新的性能度量——游程有效性（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。利用TE指标，我们证明NRST优于其可逆版本。随后，我们开发了针对NRST算法的自动化调优流程，在最小化计算成本的同时优化TE指标。该流程使得NRST能够便捷地集成到现有的概率编程语言中。我们通过大量实验证明，所提出的调优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。