Stochastic moments dynamics: a flexible finite-dimensional random perturbation of Wasserstein gradient descent
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912370794692608 |
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| author | Germain, Pierre Monmarché, Pierre |
| author_facet | Germain, Pierre Monmarché, Pierre |
| contents | For optimizing a non-convex function in finite dimension, a method is to add Brownian noise to a gradient descent, allowing for transitions between basins of attractions of different minimizers. To adapt this for optimization over a space of probability distributions requires a suitable noise. For this purpose, we introduce here a simple stochastic process where a number of moments of the distribution are following a chosen finite-dimensional diffusion process, generalizing some previous studies where the expectation of the measure is subject to a Brownian noise. The process may explode in finite time, for instance when trying to force the variance of a distribution to behave like a Brownian motion. We show, up to the possible explosion time, well-posedness and propagation of chaos for the system of mean-field interacting particles with common noise approximating the process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07448 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic moments dynamics: a flexible finite-dimensional random perturbation of Wasserstein gradient descent Germain, Pierre Monmarché, Pierre Probability For optimizing a non-convex function in finite dimension, a method is to add Brownian noise to a gradient descent, allowing for transitions between basins of attractions of different minimizers. To adapt this for optimization over a space of probability distributions requires a suitable noise. For this purpose, we introduce here a simple stochastic process where a number of moments of the distribution are following a chosen finite-dimensional diffusion process, generalizing some previous studies where the expectation of the measure is subject to a Brownian noise. The process may explode in finite time, for instance when trying to force the variance of a distribution to behave like a Brownian motion. We show, up to the possible explosion time, well-posedness and propagation of chaos for the system of mean-field interacting particles with common noise approximating the process. |
| title | Stochastic moments dynamics: a flexible finite-dimensional random perturbation of Wasserstein gradient descent |
| topic | Probability |
| url | https://arxiv.org/abs/2505.07448 |