Ergodicity of the underdamped mean-field Langevin dynamics
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Abstract (arXiv)
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 a numerical example of the algorithm to train a generative adversarial networks (GAN).
Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Jul 2020.
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Citing papers per year: 2022: 4; 2023: 2; 2024: 1.
7 papers.
- 2022Convex Analysis of the Mean Field Langevin Dynamicscited by 53
- 2022Uniform-in-time propagation of chaos for mean field Langevin dynamicscited by 23
- 2022Unbiased Estimation using Underdamped Langevin Dynamicscited by 3
- 2022Mean-field analysis for heavy ball methods: Dropout-stability, connectivity, and global convergencecited by 3
- 2024A Fisher-Rao gradient flow for entropic mean-field min-max gamescited by 3
- 2023Mean Field Optimization Problem Regularized by Fisher Informationcited by 2
- 2023Mean-field underdamped Langevin dynamics and its spacetime discretizationcited by 2
- 2024A Fisher-Rao gradient flow for entropic mean-field min-max games24 May 2024
- 2023Mean-field underdamped Langevin dynamics and its spacetime discretization26 Dec 2023
- 2023Mean Field Optimization Problem Regularized by Fisher Information12 Feb 2023
- 2022Uniform-in-time propagation of chaos for mean field Langevin dynamics6 Dec 2022
- 2022Mean-field analysis for heavy ball methods: Dropout-stability, connectivity, and global convergence13 Oct 2022
- 2022Unbiased Estimation using Underdamped Langevin Dynamics14 Jun 2022
- 2022Convex Analysis of the Mean Field Langevin Dynamics25 Jan 2022