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

arXiv: https://arxiv.org/abs/2106.04357 · HTML: https://mlsanity.com/paper/2106.04357/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2021.

## Built on by (most cited first, 4 of 4)

- [Improved Convergence Rate of Stochastic Gradient Langevin Dynamics with Variance Reduction and its Application to Optimization](https://mlsanity.com/paper/2203.16217/) (2022)
- [Unbiased and Sign Compression in Distributed Learning: Comparing Noise Resilience via SDEs](https://mlsanity.com/paper/2502.17009/) (2025)
- [Convergence Error Analysis of Reflected Gradient Langevin Dynamics for Globally Optimizing Non-Convex Constrained Problems](https://mlsanity.com/paper/2203.10215/) (2022)
- [Approximation to Deep Q-Network by Stochastic Delay Differential Equations](https://mlsanity.com/paper/2505.00382/) (2025)

## Abstract (arXiv)

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.