# Random Coordinate Underdamped Langevin Monte Carlo

arXiv: https://arxiv.org/abs/2010.11366 · HTML: https://mlsanity.com/paper/2010.11366/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2020.

## Built on by (most cited first, 6 of 6)

- [The query complexity of sampling from strongly log-concave distributions in one dimension](https://mlsanity.com/paper/2105.14163/) (2021)
- [Entropy contraction of the Gibbs sampler under log-concavity](https://mlsanity.com/paper/2410.00858/) (2024)
- [Learning Rate Free Sampling in Constrained Domains](https://mlsanity.com/paper/2305.14943/) (2023)
- [A stochastic smoothing framework for nonconvex-nonconcave minEmax problems with applications to Wasserstein distributionally robust optimization](https://mlsanity.com/paper/2502.17602/) (2025)
- [Provable Accuracy Bounds for Hybrid Dynamical Optimization and Sampling](https://mlsanity.com/paper/2410.06397/) (2024)
- [Spectral gap of Metropolis-within-Gibbs under log-concavity](https://mlsanity.com/paper/2509.26175/) (2025)

## Abstract (arXiv)

The Underdamped Langevin Monte Carlo (ULMC) is a popular Markov chain Monte Carlo sampling method. It requires the computation of the full gradient of the log-density at each iteration, an expensive operation if the dimension of the problem is high. We propose a sampling method called Random Coordinate ULMC (RC-ULMC), which selects a single coordinate at each iteration to be updated and leaves the other coordinates untouched. We investigate the computational complexity of RC-ULMC and compare it with the classical ULMC for strongly log-concave probability distributions. We show that RC-ULMC is always cheaper than the classical ULMC, with a significant cost reduction when the problem is highly skewed and high dimensional. Our complexity bound for RC-ULMC is also tight in terms of dimension dependence.