# Improving the convergence of reversible samplers

arXiv: https://arxiv.org/abs/1601.08118 · HTML: https://mlsanity.com/paper/1601.08118/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jan 2016.

## Built on by (most cited first, 8 of 8)

- [Non-Reversible Langevin Algorithms for Constrained Sampling](https://mlsanity.com/paper/2501.11743/) (2025)
- [Geometry-informed irreversible perturbations for accelerated convergence of Langevin dynamics](https://mlsanity.com/paper/2108.08247/) (2021)
- [Stable generative modeling using Schr"odinger bridges](https://mlsanity.com/paper/2401.04372/) (2024)
- [Generative Modelling with Tensor Train approximations of Hamilton--Jacobi--Bellman equations](https://mlsanity.com/paper/2402.15285/) (2024)
- [Variance Reduction for Stochastic Gradient Generalized Non-reversible Langevin Monte Carlo Algorithms](https://mlsanity.com/paper/2606.28808/) (2026)
- [Transport map unadjusted Langevin algorithms: learning and discretizing perturbed samplers](https://mlsanity.com/paper/2302.07227/) (2023)
- [Dimension-Uniform Discretization Analysis of Preconditioned Annealed Langevin Dynamics for Multimodal Gaussian Mixtures](https://mlsanity.com/paper/2605.16473/) (2026)
- [Nonreversible Gauge Fields in Fokker--Planck Dynamics: Supersymmetric Hamiltonians and Learned Finite Forces](https://mlsanity.com/paper/2606.06412/) (2026)

## Abstract (arXiv)

In Monte-Carlo methods the Markov processes used to sample a given target distribution usually satisfy detailed balance, i.e. they are time-reversible. However, relatively recent results have demonstrated that appropriate reversible and irreversible perturbations can accelerate convergence to equilibrium. In this paper we present some general design principles which apply to general Markov processes. Working with the generator of Markov processes, we prove that for some of the most commonly used performance criteria, i.e., spectral gap, asymptotic variance and large deviation functionals, sampling is improved for appropriate reversible and irreversible perturbations of some initially given reversible sampler. Moreover we provide specific constructions for such reversible and irreversible perturbations for various commonly used Markov processes, such as Markov chains and diffusions. In the case of diffusions, we make the discussion more specific using the large deviations rate function as a measure of performance.