A Sharp Uniform-in-Time Error Estimate for Stochastic Gradient Langevin Dynamics
Year: 2025
Type: article
Abstract: . We establish a sharp uniform-in-time error estimate for the stochastic gradient Langevin dynamics (SGLD), which is a widely-used sampling algorithm. Under mild assumptions, we obtain a uniform-in-time $\mathcal{O}(η^2)$ bound for the Kullback-Leibler divergence between the SGLD iteration and the Langevin diffusion, where $η$ is the step size (or learning rate). Our analysis is also valid for varying step sizes. Consequently, we are able to derive an $\mathcal{O}(\eta)$ bound for the distance between the invariant measures of the SGLD iteration and the Langevin diffusion, in terms of Wasserstein or total variation distances. Our result can be viewed as a significant improvement compared with existing analysis for SGLD in related literature.
Authors: Lei Li, Yuliang Wang
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4411194572