Learning operators on labelled conditional distributions with applications to mean field control of non exchangeable systems
Published:
Recommended citation: https://arxiv.org/pdf/2603.21683
Co-authors
Abstract
We study the approximation of operators acting on probability measures on a product space with prescribed marginal. Operators defined on this constrained measure space arise naturally in mean-field control problems with heterogeneous, non-exchangeable agents. Our main theoretical result establishes a universal approximation theorem for continuous operators on this product space. The proof combines cylindrical approximations of probability measures with a DeepONet-type branch–trunk neural architecture, yielding finite-dimensional representations of such operators. We further introduce a sampling strategy for generating training measures in the product space, enabling practical learning of such conditional mean-field operators. We apply the method to the numerical resolution of mean-field control problems with heterogeneous interactions, thereby extending previous neural approaches developed for homo- geneous (exchangeable) systems. Numerical experiments illustrate the accuracy and computa- tional effectiveness of the proposed framework.