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Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:

Jin Shi,ShangHai JiaoTong University

Inviter: 洪佳林 研究員
Title:
Random Batch Methods for Interacting Particle Systems and Consensus-based Global Non-convex Optimization in High-dimensional Machine Learning
Time & Venue:
2019.11.22 10:00-11:00 N202
Abstract:

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.

 

 

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