{
  "abstract": "We develop a stochastic mirror descent method for continuous-time McKean-Vlasov control with measure-valued controls and general Bregman regularisation. The dependence on the state law leads to a coupled Wasserstein-Bregman stability problem and to a McKean-Vlasov adjoint equation, which have no counterpart in classical stochastic control. We establish a first-order representation of the cost and prove its relative smoothness in two regimes: nonlinear dynamics with bounded cost derivatives, and affine state-law dynamics with linearly growing cost derivatives, the latter covering linear-quadratic (LQ) and more general nonquadratic models. Our regularity conditions in the control measure are formulated through directional finite increments and do not require second-order flat derivatives. We further introduce relative semiconvexity along admissible forward-backward trajectories, allowing compensation between the dynamics, running cost, and terminal cost beyond pointwise Hamiltonian convexity. This yields energy dissipation, an O(1/n) convergence rate at the convexity threshold, and geometric convergence when regularisation dominates relative nonconvexity. Explicit LQ criteria and numerical experiments illustrate the scope of the results.",
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  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32303",
  "author_total": 2,
  "authors": [
    {
      "name": "Noufel Frikha"
    },
    {
      "name": "Aymen Haouas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0jyed34q0r8j6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32303",
  "fulltext_url": null,
  "id": "0jyed34q0r8j6",
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  "landing_url": "https://hal.science/hal-05834896v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
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  "pdf_url": "https://hal.science/hal-05834896/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0jyed34q0r8j6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:00Z",
      "native_id": "hal-05834896",
      "source": "hal",
      "url": "https://hal.science/hal-05834896v1"
    },
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32303",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32303"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A stochastic mirror descent algorithm for mean-field control problems",
  "title_text": "A stochastic mirror descent algorithm for mean-field control problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/0jyed34q0r8j6",
  "venue": "HAL",
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}