Wasserstein mixing time of the unadjusted Langevin algorithm

Francesco Pedrotti; Peter A. Whalley

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arXiv · 2608.02430

Wasserstein mixing time of the unadjusted Langevin algorithm

Francesco Pedrotti·Peter A. Whalley

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Abstract

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 $\kappa \sqrt{d}/\varepsilon$, where $\kappa$ is the condition number, $d$ is the dimension, and $\varepsilon$ is the target precision: this improves by a factor of $\sqrt{d}/\varepsilon$ over the previous state-of-the-art results.

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Francesco Pedrotti, Peter A. Whalley. 2026-08-03. Wasserstein mixing time of the unadjusted Langevin algorithm. https://arxiv.org/abs/2608.02430

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