报告时间：2026年9月28日（星期一）09:30-10:30

报告地点：科教楼B座1710会议室

报  告  人：陈鹏 副教授

工作单位：南京航空航天大学

举办单位：数学学院

报告简介：

We establish normalized and self-normalized Cram\'er-type moderate deviations for stationary empirical averages $\Pi_{\eta}(h)$ generated by stochastic gradient descent (SGD) with a fixed step size $\eta$. We work in the joint asymptotic regime $\eta\to0$ and $\eta^{-1}\ll m\ll \eta^{-2}$, where $m$ denotes the number of iterations. We associate the SGD recursion with a small-noise diffusion and denote their respective invariant measures by $\pi_{1,\eta}$ and $\pi_{2,\eta}$. Using Stein's method, we decompose $\sqrt{m}\left(\Pi_{\eta}(h)-\pi_{1,\eta}(h)\right)$ into a leading martingale term and asymptotically negligible remainders. When the gradient-noise covariance matrix $\Sigma(w)$ is allowed to be unbounded, a stopping time argument, combined with stationary exponential moment estimates and concentration inequalities, yields uniform relative Gaussian tail approximations for growing deviation levels satisfying $x=o\big(m^{1/24}\wedge(m\eta)^{1/4}\wedge(\sqrt{m}\eta)^{-1}\big)$. Under an additional uniform moment condition on the gradient noise, which in particular implies that $\Sigma(w)$ is uniformly bounded, the restriction $x=o(m^{1/24})$ is removed. The results cover normalizations based on both predictable and realized quadratic variations. This is based on the joint work with Hui Jiang, Jianya Lu and Jing Wang.

报告人简介：

陈鹏，南京航空航天大学数学学院副教授。研究方向为概率极限理论，随机过程，随机算法，在The Annals of Applied Probability,SIAM Journal on Mathematical Analysis,Stochastic Processes and their Applications等杂志发表论文近20篇，主持国家自然科学基金青年项目与国际合作交流项目。