Self-normalized Cramér-type moderate deviation of stochastic gradient Langevin dynamics
Hongsheng Dai, Xiequan Fan, Jianya Lu · Journal of Applied Probability · 2026
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.