Self-normalized Cramér-type moderate deviation of stochastic gradient Langevin dynamics
Abstract
Abstract In this paper, we study the self-normalized Cramér-type moderate deviation of the empirical measure of the stochastic gradient Langevin dynamics (SGLD). Consequently, we also derive the Berry–Esseen bound for the SGLD. Our approach is by constructing a stochastic differential equation to approximate the SGLD and then applying Stein’s method to decompose the empirical measure into a martingale difference series sum and a negligible remainder term.
Fields of Study & Subjects
Quantum Information and Cryptography
Theoretical and Computational Physics
Quantum optics and atomic interactions
Publication details
- Journal / source
- Journal of Applied Probability
- Volume
- 63
- Issue
- 3
- Pages
- 1034–1061
- Publication date
- 2 March 2026
- Language
- EN