663	RWTH Publication No: 989626        2024
TITLE	Dynamics of measure-valued agents in the space of probabilities
AUTHORS	Giacomo Borghi, Michael Herty, Andrey Stavitskiy
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	multi-agent systems, Wasserstein space, consensus dynamics, measure differential inclusions, consensus-based optimization