Uniform-in-time propagation of chaos for mean field Langevin dynamics
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
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| _version_ | 1866917061801803776 |
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| author | Chen, Fan Ren, Zhenjie Wang, Songbo |
| author_facet | Chen, Fan Ren, Zhenjie Wang, Songbo |
| contents | We study the mean field Langevin dynamics and the associated particle system. By assuming the functional convexity of the energy, we obtain the $L^p$-convergence of the marginal distributions towards the unique invariant measure for the mean field dynamics. Furthermore, we prove the uniform-in-time propagation of chaos in both the $L^2$-Wasserstein metric and relative entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_03050 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Uniform-in-time propagation of chaos for mean field Langevin dynamics Chen, Fan Ren, Zhenjie Wang, Songbo Probability Machine Learning 60J60, 60K35 (Primary) 35B40, 35Q83, 35Q84 (Secondary) We study the mean field Langevin dynamics and the associated particle system. By assuming the functional convexity of the energy, we obtain the $L^p$-convergence of the marginal distributions towards the unique invariant measure for the mean field dynamics. Furthermore, we prove the uniform-in-time propagation of chaos in both the $L^2$-Wasserstein metric and relative entropy. |
| title | Uniform-in-time propagation of chaos for mean field Langevin dynamics |
| topic | Probability Machine Learning 60J60, 60K35 (Primary) 35B40, 35Q83, 35Q84 (Secondary) |
| url | https://arxiv.org/abs/2212.03050 |