arXiv preprint, 2025.
In brief
Underdamped (second-order) Langevin dynamics sample faster than overdamped ones; this paper goes further and discretizes P-th order Langevin dynamics for any P ≥ 3, combining splitting with accurate integration of the exactly solvable parts. The resulting samplers come with Wasserstein convergence guarantees for smooth log-concave targets, with a dependence on dimension and accuracy that improves as the order grows.
Cite
@misc{dang2025highorder,
title = {High-order Langevin Monte Carlo algorithms},
author = {Thanh Dang and Mert Gürbüzbalaban and Mohammad Rafiqul Islam and Nian Yao and Lingjiong Zhu},
year = {2025},
howpublished = {arXiv preprint arXiv:2508.17545},
}Relatedsame topics