Wasserstein mixing time of the unadjusted Langevin algorithm

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.

Computation (stat.CO); Machine Learning (cs.LG); Numerical Analysis (math.NA); Probability (math.PR)

arXiv:2608.02430 [stat.CO]

(or arXiv:2608.02430v1 [stat.CO] for this version)

https://doi.org/10.48550/arXiv.2608.02430 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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