Automatic Regenerative Simulation via Non-Reversible Simulated Tempering

TL;DR

This paper introduces a non-reversible Simulated Tempering algorithm with an automated tuning method, improving efficiency and robustness for complex probabilistic models by optimizing a new performance metric called Tour Effectiveness.

Contribution

It develops a non-reversible version of Simulated Tempering, introduces a theoretical analysis including a novel performance metric, and provides an automated tuning procedure for practical implementation.

Findings

NRST outperforms reversible ST in efficiency.

Automated tuning improves robustness across models.

Tour Effectiveness correlates with estimation accuracy.

Abstract

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.