# Accelerating Langevin Monte Carlo Sampling: A Large Deviations Analysis

arXiv: https://arxiv.org/abs/2503.19066 · HTML: https://mlsanity.com/paper/2503.19066/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 59 references that are in the map.
- First posted on arXiv 24 Mar 2025.

## Builds on (most cited first, 30 of 34)

- [Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysis](https://mlsanity.com/paper/1702.03849/) (2017)
- [Theoretical guarantees for approximate sampling from smooth and log-concave densities](https://mlsanity.com/paper/1412.7392/) (2014)
- [Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1507.05021/) (2015)
- [A Complete Recipe for Stochastic Gradient MCMC](https://mlsanity.com/paper/1506.04696/) (2015)
- [High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1605.01559/) (2016)
- [Underdamped Langevin MCMC: A non-asymptotic analysis](https://mlsanity.com/paper/1707.03663/) (2017)
- [User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient](https://mlsanity.com/paper/1710.00095/) (2017)
- [Convergence of Langevin MCMC in KL-divergence](https://mlsanity.com/paper/1705.09048/) (2017)
- [Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau](https://mlsanity.com/paper/1612.07471/) (2016)
- [Sharp convergence rates for Langevin dynamics in the nonconvex setting](https://mlsanity.com/paper/1805.01648/) (2018)
- [On sampling from a log-concave density using kinetic Langevin diffusions](https://mlsanity.com/paper/1807.09382/) (2018)
- [Mirrored Langevin Dynamics](https://mlsanity.com/paper/1802.10174/) (2018)
- [Efficient constrained sampling via the mirror-Langevin algorithm](https://mlsanity.com/paper/2010.16212/) (2020)
- [Sampling from a log-concave distribution with Projected Langevin Monte Carlo](https://mlsanity.com/paper/1507.02564/) (2015)
- [Sampling from a log-concave distribution with compact support with proximal Langevin Monte Carlo](https://mlsanity.com/paper/1705.08964/) (2017)
- [Exponential ergodicity of mirror-Langevin diffusions](https://mlsanity.com/paper/2005.09669/) (2020)
- [The Mirror Langevin Algorithm Converges with Vanishing Bias](https://mlsanity.com/paper/2109.12077/) (2021)
- [High-Order Langevin Diffusion Yields an Accelerated MCMC Algorithm](https://mlsanity.com/paper/1908.10859/) (2019)
- [Primal Dual Interpretation of the Proximal Stochastic Gradient Langevin Algorithm](https://mlsanity.com/paper/2006.09270/) (2020)
- [Non-convex Learning via Replica Exchange Stochastic Gradient MCMC](https://mlsanity.com/paper/2008.05367/) (2020)
- [Fractional Underdamped Langevin Dynamics: Retargeting SGD with Momentum under Heavy-Tailed Gradient Noise](https://mlsanity.com/paper/2002.05685/) (2020)
- [Projected Stochastic Gradient Langevin Algorithms for Constrained Sampling and Non-Convex Learning](https://mlsanity.com/paper/2012.12137/) (2020)
- [Global Convergence of Stochastic Gradient Hamiltonian Monte Carlo for Non-Convex Stochastic Optimization: Non-Asymptotic Performance Bounds and Momentum-Based Acceleration](https://mlsanity.com/paper/1809.04618/) (2018)
- [Deep Learning: A Bayesian Perspective](https://mlsanity.com/paper/1706.00473/) (2017)
- [Decentralized Stochastic Gradient Langevin Dynamics and Hamiltonian Monte Carlo](https://mlsanity.com/paper/2007.00590/) (2020)
- [Accelerating Nonconvex Learning via Replica Exchange Langevin Diffusion](https://mlsanity.com/paper/2007.01990/) (2020)
- [Fractional Langevin Monte Carlo: Exploring L'evy Driven Stochastic Differential Equations for Markov Chain Monte Carlo](https://mlsanity.com/paper/1706.03649/) (2017)
- [Penalized Overdamped and Underdamped Langevin Monte Carlo Algorithms for Constrained Sampling](https://mlsanity.com/paper/2212.00570/) (2022)
- [Breaking Reversibility Accelerates Langevin Dynamics for Global Non-Convex Optimization](https://mlsanity.com/paper/1812.07725/) (2018)
- [Generalized EXTRA stochastic gradient Langevin dynamics](https://mlsanity.com/paper/2412.01993/) (2024)

## Built on by (most cited first, 4 of 4)

- [Accelerating Constrained Sampling: A Large Deviations Approach](https://mlsanity.com/paper/2506.07816/) (2025)
- [Decentralized Proximal Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/2605.00723/) (2026)
- [Particle-based Generalised Stochastic Optimisation](https://mlsanity.com/paper/2608.02844/) (2026)
- [Accelerating Non-Smooth and Heavy-Tailed Sampling](https://mlsanity.com/paper/2610.11139/) (2026)

## Abstract (arXiv)

Langevin algorithms are popular Markov chain Monte Carlo methods that are often used to solve high-dimensional large-scale sampling problems in machine learning. The most classical Langevin Monte Carlo algorithm is based on the overdamped Langevin dynamics. There are many variants of Langevin dynamics that often show superior performance in practice. In this paper, we provide a unified approach to study the acceleration of the variants of the overdamped Langevin dynamics through the lens of large deviations theory. Numerical experiments using both synthetic and real data are provided to illustrate the efficiency of these variants.