ERGODICITY OF THE UNDERDAMPED MEAN-FIELD LANGEVIN DYNAMICS

被引：1

作者：

Kazeykina, Anna ^{[1
]}

Ren, Zhenjie ^{[2
]}

Tan, Xiaolu ^{[3
]}

Yang, Junjian ^{[4
]}

机构：

[1] Univ Paris Saclay, Fac Sci Orsay, Dept Math, Paris, France

[2] PSL, Univ Paris Dauphine, CEREMADE, Paris, France

[3] Chinese Univ Hong Kong, Dept Math, Hong Kong, Peoples R China

[4] Vienna Univ Technol, Fak Math & Geoinformat, FAM, Vienna, Austria

来源：

ANNALS OF APPLIED PROBABILITY | 2024年 / 34卷 / 03期

关键词：

Underdamped mean-field Langevin dynamics; ergodicity; coupling; GAN; EXPONENTIAL CONVERGENCE; MOLECULAR-DYNAMICS; KINETIC-EQUATIONS; CONTRACTION RATES; TIME-REVERSAL; HYPOCOERCIVITY; PROPAGATION; EQUILIBRIUM; COUPLINGS; BEHAVIOR;

D O I：

10.1214/23-AAP2036

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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).

引用

页码：3181 / 3226

页数：46

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