Wasserstein mixing time of the unadjusted Langevin algorithm
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Abstract (arXiv)
We provide new estimates in Wasserstein distance for the asymptotic bias of the unadjusted Langevin algorithm, in the classical setting of log-smooth strongly log-concave measures. Our bound implies a Wasserstein mixing time of order kappa √d/varepsilon, where kappa is the condition number, d is the dimension, and varepsilon is the target precision: this improves by a factor of √d/varepsilon over the previous state-of-the-art results.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 11 of its 24 references that are in the map. First posted on arXiv 3 Aug 2026.
Builds on
11 of 24 references.
References · 11
- 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 224
- 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 206
- 2015Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmcited by 195
- 2016High-dimensional Bayesian inference via the Unadjusted Langevin Algorithmcited by 144
- 2018Analysis of Langevin Monte Carlo via convex optimizationcited by 126
- 2018Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problemcited by 123
- 2017User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradientcited by 116
- 2021Sqrt(d) Dimension Dependence of Langevin Monte Carlocited by 25
- 2021Asymptotic bias of inexact Markov Chain Monte Carlo methods in high dimensioncited by 11
- 2024Convergence of Unadjusted Langevin in High Dimensions: Delocalization of Biascited by 4
- 2026Improved Guarantees for Langevin Monte Carlo with Average Smoothnesscited by 2
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Citing papers per year: 2026: 1.
1 paper.