# Constrained Ensemble Langevin Monte Carlo

arXiv: https://arxiv.org/abs/2102.04279 · HTML: https://mlsanity.com/paper/2102.04279/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 43 references that are in the map.
- First posted on arXiv 8 Feb 2021.

## Builds on (most cited first, 11 of 11)

- [Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices](https://mlsanity.com/paper/1903.08568/) (2019)
- [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)
- [Analysis of Langevin Monte Carlo via convex optimization](https://mlsanity.com/paper/1802.09188/) (2018)
- [Log-concave sampling: Metropolis-Hastings algorithms are fast](https://mlsanity.com/paper/1801.02309/) (2018)
- [User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient](https://mlsanity.com/paper/1710.00095/) (2017)
- [On sampling from a log-concave density using kinetic Langevin diffusions](https://mlsanity.com/paper/1807.09382/) (2018)
- [On the Theory of Variance Reduction for Stochastic Gradient Monte Carlo](https://mlsanity.com/paper/1802.05431/) (2018)
- [Ensemble preconditioning for Markov chain Monte Carlo simulation](https://mlsanity.com/paper/1607.03954/) (2016)
- [MALA-within-Gibbs samplers for high-dimensional distributions with sparse conditional structure](https://mlsanity.com/paper/1908.09429/) (2019)
- [Continuous Limits for Constrained Ensemble Kalman Filter](https://mlsanity.com/paper/1912.08406/) (2019)

## Built on by (most cited first, 1 of 1)

- [A Metropolis-Adjusted Langevin Algorithm for Sampling Jeffreys Prior](https://mlsanity.com/paper/2504.06372/) (2025)

## Abstract (arXiv)

The classical Langevin Monte Carlo method looks for samples from a target distribution by descending the samples along the gradient of the target distribution. The method enjoys a fast convergence rate. However, the numerical cost is sometimes high because each iteration requires the computation of a gradient. One approach to eliminate the gradient computation is to employ the concept of ``ensemble." A large number of particles are evolved together so the neighboring particles provide gradient information to each other. In this article, we discuss two algorithms that integrate the ensemble feature into LMC and the associated properties. In particular, we find that if one directly surrogates the gradient using the ensemble approximation, the algorithm, termed Ensemble Langevin Monte Carlo, is unstable due to a high variance term. If the gradients are replaced by the ensemble approximations only in a constrained manner, to protect from the unstable points, the algorithm, termed Constrained Ensemble Langevin Monte Carlo, resembles the classical LMC up to an ensemble error but removes most of the gradient computation.