报告人：薄立军（西安电子科技大学）

邀请人：吴付科

报告时间：2021年6月24日（星期四）16：00-18：00

报告地点： 科技楼（南楼）611室

报告题目：A Mean-Field Stochastic Control Problem in Deep Residual Learning

报告摘要：We study a class of stochastic optimization problems of the mean-field type arising in the optimal training of a deep residual neural network. We estimate the training weights of the network as the optimal relaxed control of a sampling problem, where a population risk criterion is minimized. We establish the existence of optimal relaxed controls when the training set has finite size. The core of our paper is to prove, via $\Gamma$-convergence, that the minimizer of the sampled relaxed problem converges to that of the limiting optimization problem, as the number of training samples grows large. We connect the limit of the sampled objective functional to the unique solution, in the trajectory sense, of a nonlinear Fokker-Planck-Kolmogorov (FPK) equation in a random environment.

This is a joint work with A. Capponi (Columbia Univ.) and Huafu Liao (NUS).

报告人简介：薄立军，西安电子科技大学数学与统计学院教授，研究方向为随机分析、随机控制与金融数学。目前已在国际公认的概率统计、金融数学、管理和运筹学权威期刊Math. Finan., Finan. & Stoch., SIAM J. Finan. Math., SIAM J. Control & Optim, Math. Opers. Res., J.Banking & Finan., Appl. Math. & Optim., J. Dyn. Econ. & Contr., Queueing Syst., J. Theor. Probab.上发表学术论文30余篇。目前担任中国概率统计学会会刊《应用概率统计》编委；美国数学科学研究所(AIMS)旗舰期刊《J. Dynamics & Games》Associate Editor.