Self-normalized Cram\'er-type Moderate Deviation of Stochastic Gradient Langevin Dynamics
Probability
2026-03-04 v1 Statistics Theory
Statistics Theory
Abstract
In this paper, we study the self-normalized Cram\'er-type moderate deviation of the empirical measure of the stochastic gradient Langevin dynamics (SGLD). Consequently, we also derive the Berry-Esseen bound for SGLD. Our approach is by constructing a stochastic differential equation (SDE) to approximate the SGLD and then applying Stein's method as developed in [9,19], to decompose the empirical measure into a martingale difference series sum and a negligible remainder term.
Cite
@article{arxiv.2410.22047,
title = {Self-normalized Cram\'er-type Moderate Deviation of Stochastic Gradient Langevin Dynamics},
author = {Hongsheng Dai and Xiequan Fan and Jianya Lu},
journal= {arXiv preprint arXiv:2410.22047},
year = {2026}
}