An Occupation-Measure and Frank-Wolfe Framework for Heterogeneous Mean-Field Control
Abstract
Heterogeneous mean-field control (MFC) involves multiple interacting populations with distinct dynamics, control constraints, and coupling structures. We develop a heterogeneous occupation-measure mean-field control (OM-MFC) framework that reformulates the population-distribution control problem as an optimization problem over occupation measures. In this representation, potentially nonlinear dynamics enter through linear weak Liouville constraints, while nonlocal inter-population interactions become structured bilinear functionals of the occupation-measure marginals. Exploiting this structure, we derive a Frank--Wolfe (FW) method and show that its linear minimization oracle decomposes into independent population-wise optimal control problems once the current population distributions are fixed, enabling parallel computation without an a priori discretization of the measure space. We further establish a sufficient convexity condition based on the symmetrized matrix-valued interaction kernel, under which Frank--Wolfe with an exact oracle admits the standard O(1/k) convergence rate. Numerical examples on heterogeneous UAV coordination and three-dimensional search-and-rescue illustrate the framework both within the certified convex regime and for directional interactions beyond that regime.
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BibTeX
@misc{yu2026occupationmeasure,
title = {{An Occupation-Measure and Frank-Wolfe Framework for Heterogeneous Mean-Field Control}},
author = {Di Yu and Sixiong You and Chaoying Pei},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.09907},
eprint = {2607.09907},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.09907},
}
RIS
TY - UNPB
TI - An Occupation-Measure and Frank-Wolfe Framework for Heterogeneous Mean-Field Control
AU - Di Yu
AU - Sixiong You
AU - Chaoying Pei
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2607.09907
UR - https://arxiv.org/abs/2607.09907
AB - Heterogeneous mean-field control (MFC) involves multiple interacting populations with distinct dynamics, control constraints, and coupling structures. We develop a heterogeneous occupation-measure mean-field control (OM-MFC) framework that reformulates the population-distribution control problem as an optimization problem over occupation measures. In this representation, potentially nonlinear dynamics enter through linear weak Liouville constraints, while nonlocal inter-population interactions become structured bilinear functionals of the occupation-measure marginals. Exploiting this structure, we derive a Frank--Wolfe (FW) method and show that its linear minimization oracle decomposes into independent population-wise optimal control problems once the current population distributions are fixed, enabling parallel computation without an a priori discretization of the measure space. We further establish a sufficient convexity condition based on the symmetrized matrix-valued interaction kernel, under which Frank--Wolfe with an exact oracle admits the standard O(1/k) convergence rate. Numerical examples on heterogeneous UAV coordination and three-dimensional search-and-rescue illustrate the framework both within the certified convex regime and for directional interactions beyond that regime.
ER -