Accelerated Parallel Tempering via Neural Transports

TL;DR

This paper introduces a neural transport framework to accelerate Parallel Tempering MCMC, improving sampling efficiency for complex distributions while maintaining theoretical guarantees.

Contribution

It proposes integrating neural samplers into Parallel Tempering to reduce overlap requirements and computational costs, a novel approach in MCMC acceleration.

Findings

Improves sample quality in multimodal problems.

Reduces computational cost compared to classical PT.

Enables efficient free energy estimation.

Abstract

Markov Chain Monte Carlo (MCMC) algorithms are essential tools in computational statistics for sampling from unnormalised probability distributions, but can be fragile when targeting high-dimensional, multimodal, or complex target distributions. Parallel Tempering (PT) enhances MCMC's sample efficiency through annealing and parallel computation, propagating samples from tractable reference distributions to intractable targets via state swapping across interpolating distributions. The effectiveness of PT is limited by the often minimal overlap between adjacent distributions in challenging problems, which requires increasing the computational resources to compensate. We introduce a framework that accelerates PT by leveraging neural samplers -- including normalising flows, diffusion models, and controlled diffusions -- to reduce the required overlap. Our approach utilises neural samplers in parallel, circumventing the computational burden of neural samplers while preserving the asymptotic consistency of classical PT. We demonstrate theoretically and empirically on a variety of multimodal sampling problems that our method improves sample quality, reduces the computational cost compared to classical PT, and enables efficient free energy/normalising constant estimation.