Mirror Mean-Field Langevin Dynamics
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913138405801984 |
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| author | Gu, Anming Kim, Juno |
| author_facet | Gu, Anming Kim, Juno |
| contents | The mean-field Langevin dynamics (MFLD) minimizes an entropy-regularized nonlinear convex functional on the Wasserstein space over $\mathbb{R}^d$, and has gained attention recently as a model for the gradient descent dynamics of interacting particle systems such as infinite-width two-layer neural networks. However, many problems of interest have constrained domains, which are not solved by existing mean-field algorithms due to the global diffusion term. We study the optimization of probability measures constrained to a convex subset of $\mathbb{R}^d$ by proposing the \emph{mirror mean-field Langevin dynamics} (MMFLD), an extension of MFLD to the mirror Langevin framework. We obtain linear convergence guarantees for the continuous MMFLD via a uniform log-Sobolev inequality, and uniform-in-time propagation of chaos results for its time- and particle-discretized counterpart. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02621 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mirror Mean-Field Langevin Dynamics Gu, Anming Kim, Juno Machine Learning Optimization and Control The mean-field Langevin dynamics (MFLD) minimizes an entropy-regularized nonlinear convex functional on the Wasserstein space over $\mathbb{R}^d$, and has gained attention recently as a model for the gradient descent dynamics of interacting particle systems such as infinite-width two-layer neural networks. However, many problems of interest have constrained domains, which are not solved by existing mean-field algorithms due to the global diffusion term. We study the optimization of probability measures constrained to a convex subset of $\mathbb{R}^d$ by proposing the \emph{mirror mean-field Langevin dynamics} (MMFLD), an extension of MFLD to the mirror Langevin framework. We obtain linear convergence guarantees for the continuous MMFLD via a uniform log-Sobolev inequality, and uniform-in-time propagation of chaos results for its time- and particle-discretized counterpart. |
| title | Mirror Mean-Field Langevin Dynamics |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2505.02621 |