Self-normalized Cramér-type Moderate Deviation of Stochastic Gradient Langevin Dynamics

2024/10/29 by Dai, Hongsheng, Fan, Xiequan, Lu, Jianya · 1 citation
#FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2410.22047

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 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.

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