Random Batch Methods for Interacting Particle Systems and its Applications in Consensus-based High Dimensional Global Optimization in Machine Learning

主讲人：金石 上海交通大学教授

时间：2019年10月25日15:30

地点：徐汇校区3号楼332室

举办单位：数理学院

主讲人介绍：金石，现为上海交通大学自然科学研究院院长。先后获北京大学学士学位，美国亚利桑那大学博士学位，历任美国纽约大学库朗数学研究所博士后，美国佐治亚理工学院助理教授、副教授，美国威斯康星大学（麦迪逊）正教授，数学系系主任，Vilas 杰出成就教授，上海交通大学数学系讲席教授、系主任。他曾获得冯康科学计算奖，国家自然科学基金杰出青年基金(海外），国际华人数学家大会晨兴数学银奖。他是美国数学会（AMS）首批会士，工业与应用数学学会(SIAM)会士，及2018年国际数学家大会邀请报告人。

内容介绍：We develop random batch methods for interacting particle systems with large number of particles. These methods use small but random batches for particle interactions, thus the computational cost is reduced from O(N^2) per time step to O(N), for a system with N particles with binary interactions. For one of the methods, we give a particle number independent error estimate under some special interactions. Then, we apply these methods to some representative problems in mathematics, physics, social and data sciences, including the Dyson Brownian motion from random matrix theory, Thomson's problem, distribution of wealth, opinion dynamics and clustering. Numerical results show that the methods can capture both the transient solutions and the global equilibrium in these problems. We also apply this method and improve the consensus-based global optimization algorithm for high dimensional machine learning problems. This method does not require taking gradient in finding global minima for non-convex functions in high dimensions.