{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.09907",
  "author_total": 3,
  "authors": [
    {
      "name": "Di Yu"
    },
    {
      "name": "Sixiong You"
    },
    {
      "name": "Chaoying Pei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ttyp7dk9d8n9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.09907",
  "fulltext_url": null,
  "id": "1ttyp7dk9d8n9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.09907",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7168236603",
  "pdf_url": "https://arxiv.org/pdf/2607.09907",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ttyp7dk9d8n9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2607.09907",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.09907"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "An Occupation-Measure and Frank-Wolfe Framework for Heterogeneous Mean-Field Control",
  "title_text": "An Occupation-Measure and Frank-Wolfe Framework for Heterogeneous Mean-Field Control",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/1ttyp7dk9d8n9",
  "venue": "arXiv",
  "versions": []
}