Dynamics of measure-valued agents in the space of probabilities
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929414389891072 |
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| author | Borghi, Giacomo Herty, Michael Stavitskiy, Andrey |
| author_facet | Borghi, Giacomo Herty, Michael Stavitskiy, Andrey |
| contents | Motivated by the development of dynamics in probability spaces, we propose a novel multi-agent dynamic of consensus type where each agent is a probability measure. The agents move instantaneously towards a weighted barycenter of the ensemble according to the 2-Wasserstein metric. We mathematically describe the evolution as a system of measure differential inclusions and show the existence of solutions for compactly supported initial data. Inspired by the consensus-based optimization, we apply the multi-agent system to solve a minimization problem over the space of probability measures. In the small numerical example, each agent is described by a particle approximation and aims to approximate a target measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06389 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamics of measure-valued agents in the space of probabilities Borghi, Giacomo Herty, Michael Stavitskiy, Andrey Analysis of PDEs 34G20, 35D30, 49Q22 Motivated by the development of dynamics in probability spaces, we propose a novel multi-agent dynamic of consensus type where each agent is a probability measure. The agents move instantaneously towards a weighted barycenter of the ensemble according to the 2-Wasserstein metric. We mathematically describe the evolution as a system of measure differential inclusions and show the existence of solutions for compactly supported initial data. Inspired by the consensus-based optimization, we apply the multi-agent system to solve a minimization problem over the space of probability measures. In the small numerical example, each agent is described by a particle approximation and aims to approximate a target measure. |
| title | Dynamics of measure-valued agents in the space of probabilities |
| topic | Analysis of PDEs 34G20, 35D30, 49Q22 |
| url | https://arxiv.org/abs/2407.06389 |