# Is There an Analog of Nesterov Acceleration for MCMC?

arXiv: https://arxiv.org/abs/1902.00996 · HTML: https://mlsanity.com/paper/1902.00996/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Feb 2019.

## Built on by (most cited first, 19 of 19)

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- [An Improved Analysis of Langevin Algorithms with Prior Diffusion for Non-Log-Concave Sampling](https://mlsanity.com/paper/2403.06183/) (2024)
- [One-Step Generative Modeling via Unbalanced Optimal Transport](https://mlsanity.com/paper/2609.32708/) (2026)

## Abstract (arXiv)

We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization on the space of probability measures, with Kullback-Leibler (KL) divergence as the objective functional. We show that an underdamped form of the Langevin algorithm performs accelerated gradient descent in this metric. To characterize the convergence of the algorithm, we construct a Lyapunov functional and exploit hypocoercivity of the underdamped Langevin algorithm. As an application, we show that accelerated rates can be obtained for a class of nonconvex functions with the Langevin algorithm.