Mean-field underdamped Langevin dynamics and its spacetime discretization
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866911771818721280 |
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| author | Fu, Qiang Wilson, Ashia |
| author_facet | Fu, Qiang Wilson, Ashia |
| contents | We propose a new method called the N-particle underdamped Langevin algorithm for optimizing a special class of non-linear functionals defined over the space of probability measures. Examples of problems with this formulation include training mean-field neural networks, maximum mean discrepancy minimization and kernel Stein discrepancy minimization. Our algorithm is based on a novel spacetime discretization of the mean-field underdamped Langevin dynamics, for which we provide a new, fast mixing guarantee. In addition, we demonstrate that our algorithm converges globally in total variation distance, bridging the theoretical gap between the dynamics and its practical implementation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16360 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mean-field underdamped Langevin dynamics and its spacetime discretization Fu, Qiang Wilson, Ashia Computation Optimization and Control Statistics Theory Machine Learning We propose a new method called the N-particle underdamped Langevin algorithm for optimizing a special class of non-linear functionals defined over the space of probability measures. Examples of problems with this formulation include training mean-field neural networks, maximum mean discrepancy minimization and kernel Stein discrepancy minimization. Our algorithm is based on a novel spacetime discretization of the mean-field underdamped Langevin dynamics, for which we provide a new, fast mixing guarantee. In addition, we demonstrate that our algorithm converges globally in total variation distance, bridging the theoretical gap between the dynamics and its practical implementation. |
| title | Mean-field underdamped Langevin dynamics and its spacetime discretization |
| topic | Computation Optimization and Control Statistics Theory Machine Learning |
| url | https://arxiv.org/abs/2312.16360 |