ERGODICITY OF THE UNDERDAMPED MEAN-FIELD LANGEVIN DYNAMICS

• 成果类型: Article
• 署名作者: Kazeykina, Anna; Ren, Zhenjie; Tan, Xiaolu; Yang, Junjian
• 署名单位: Universite Paris Saclay; Universite PSL; Universite Paris-Dauphine; Chinese University of Hong Kong; Technische Universitat Wien
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP2036
• 发表日期: 2024
• 页码: 3181-3226
• 关键词: exponential convergence; molecular-dynamics; kinetic-equations; contraction rates; time-reversal; hypocoercivity; propagation; equilibrium; Couplings; BEHAVIOR

摘要

We study the long time behavior of an underdamped mean -field Langevin (MFL) equation, and provide a general convergence as well as an exponential convergence rate result under different conditions. The results on the MFL equation can be applied to study the convergence of the Hamiltonian gradient descent algorithm for the overparametrized optimization. We then provide some numerical examples of the algorithm to train a generative adversarial network (GAN).