Approximation to stochastic variance reduced gradient Langevin dynamics by stochastic delay differential equations

TL;DR

This paper introduces a novel approximation method for stochastic variance reduced gradient Langevin dynamics using stochastic delay differential equations, providing a uniform error bound in Wasserstein-1 distance.

Contribution

It presents a new approximation framework employing stochastic delay differential equations and advanced calculus techniques, improving understanding of the dynamics.

Findings

Established a uniform error bound in Wasserstein-1 distance

Developed a refined Lindeberg principle for analysis

Applied Malliavin calculus to stochastic dynamics

Abstract

We study in this paper a weak approximation to stochastic variance reduced gradient Langevin dynamics by stochastic delay differential equations in Wasserstein-1 distance, and obtain a uniform error bound. Our approach is via a refined Lindeberg principle and Malliavin calculus.