{
  "abstract": "We study objective-only optimization of possibly nonconvex and nonsmooth functionals over probability measures on a separable Hilbert space, allowing the optimizer to be intrinsically non-Dirac. We introduce SCMO (Stochastic Control Measure Optimizer), a gradient-free particle method derived from entropy regularized stochastic control. After finite-particle and Galerkin approximations, a Cole--Hopf transform represents the optimal feedback as a Gibbs-weighted terminal displacement. SCMO approximates this feedback by sampling context clouds, replacing one particle at a time with candidate draws, scoring the resulting empirical measures, and applying exponential reweighting. SCMO uses separate covariances for candidate proposals and particle updates, termed matched when equal and nonmatched otherwise; our analysis covers both settings. In the matched case, we establish PDE-free qualitative convergence and a projection-first quantitative bound separating particle, Galerkin-projection, and entropy-regularization errors. For the practical multi-context implementation with nonmatched covariance, we prove finite-candidate consistency and show that the signed, curvature-dependent effect of nonmatched covariance can reduce the resulting upper bound on the approximation error. Finally, experiments on function-space, trajectory-law, and contact-rich manipulation problems show that SCMO handles nonsmooth and nonconvex objectives, escapes suboptimal local basins, and recovers prescribed multimodal, non-Dirac law structure. Code for reproducing our experimental results is available at https://github.com/HenryCHEUNG7373/SCMO.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14548",
  "author_total": 2,
  "authors": [
    {
      "name": "Hang Cheung"
    },
    {
      "name": "Jinniao Qiu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cfhz2z9m6wmft.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14548",
  "fulltext_url": null,
  "id": "cfhz2z9m6wmft",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14548",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Adaptive Dynamic Programming Control"
    ]
  ],
  "openalex": "W7213327471",
  "pdf_url": "https://arxiv.org/pdf/2609.14548",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cfhz2z9m6wmft.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14548",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14548"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "SCMO: Stochastic Control for Optimization over Probability Measures on Infinite-Dimensional Spaces",
  "title_text": "SCMO: Stochastic Control for Optimization over Probability Measures on Infinite-Dimensional Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/cfhz2z9m6wmft",
  "venue": "arXiv",
  "versions": []
}