{
  "abstract": "We consider control-affine optimal control problems on the torus, where the dynamics and cost functions are only accessed through samples. Starting from a weak formulation of such problems, we derive a dual, a primal, and a primal-dual formulation, compatible with stochastic optimization. We show convergence of stochastic first-order methods to the optimal value under generic conditions. In addition, we introduce a computable metric that upper-bounds the performance of suboptimal controllers produced during optimization, under additional regularity assumptions. Preliminary results show that the method can efficiently solve a simple control problem. Finally, we discuss conditions for the boundedness of the optimal occupation measure, a key assumption for the primal and primal-dual approaches.",
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  "article_type": null,
  "arxiv": "2609.29265",
  "author_total": 3,
  "authors": [
    {
      "name": "Eloïse Berthier"
    },
    {
      "name": "Ziad Kobeissi"
    },
    {
      "name": "Francis Bach"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c8avdazh3kp3z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29265",
  "fulltext_url": null,
  "id": "c8avdazh3kp3z",
  "issns": [],
  "landing_url": "https://hal.science/hal-05762216v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "1703|Adaptive Dynamic Programming Control"
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  "openalex": "W7214385955",
  "pdf_url": "https://hal.science/hal-05762216/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c8avdazh3kp3z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:40Z",
      "native_id": "hal-05762216",
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      "url": "https://hal.science/hal-05762216v1"
    },
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29265",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29265"
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  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A Stochastic Optimization Approach to Control-Affine Optimal Control Problems",
  "title_text": "A Stochastic Optimization Approach to Control-Affine Optimal Control Problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/c8avdazh3kp3z",
  "venue": "HAL",
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}