Dynamics of measure-valued agents in the space of probabilities
Analysis of PDEs
2024-07-10 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2407.06389,
title = {Dynamics of measure-valued agents in the space of probabilities},
author = {Giacomo Borghi and Michael Herty and Andrey Stavitskiy},
journal= {arXiv preprint arXiv:2407.06389},
year = {2024}
}