报告人:杜恺 副教授 (复旦大学)
主持人:李娜教授 betway必威副经理
报告地点:燕山校区1号教学楼1502
报告时间:2024年4月22日(星期一)10:30-11:30
主办单位:betway必威
摘要:
For a certain class of McKean–Vlasov processes, we introduce proxy processes that substitute the mean-field interaction with self-interaction, employing a weighted occupation measure. Our study encompasses two key achievements. First, we demonstrate the ergodicity of the self-interacting dynamics, under broad conditions, by applying the reflection coupling method. Second, in scenarios where the drifts are negative intrinsic gradients of convex mean-field potential functionals, we use entropy and functional inequalities to demonstrate that the stationary measures of the self-interacting processes approximate the invariant measures of the corresponding McKean–Vlasov processes. As an application, we show how to learn the optimal weights of a two-layer neural network by training a single neuron.
报告人简介:
杜恺,复旦大学上海数学中心长聘副教授、博士生导师;2011年获复旦大学博士学位,曾任职于苏黎世联邦理工学院(ETH)、澳大利亚Wollongong大学;主要研究方向包括随机分析、偏微分方程、最优控制、强化学习等,成果发表于PTRF、TAMS、SICON、JDE等国际主流期刊;2019年获聘上海市“东方学者”特聘教授,2022年入选国家优秀青年科学基金项目。