{
  "abstract": "We develop a deep Pontryagin learning framework for high-dimensional continuous-time stochastic control problems that naturally accommodates jump-diffusions. In contrast to direct policy optimization, which repeatedly differentiates the objective through the entire time-discretized dynamics, our method separates adjoint learning from policy improvement by explicitly incorporating state-sensitivity information from the Pontryagin stochastic maximum principle. For a fixed Markov control, we first compute pathwise adjoint labels by backpropagating the reward through time along simulated state trajectories, and project these labels onto the Markov state through a supervised regression step. The control is then updated by enforcing the pointwise Hamiltonian stationarity condition. We prove that the resulting projected adjoint process satisfies a discrete-time Pontryagin principle and converges, as the time step tends to zero, to the solution of the corresponding continuous-time adjoint backward stochastic differential equation. Numerical experiments illustrate the accuracy, stability, and scalability of the approach.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26718",
  "author_total": 2,
  "authors": [
    {
      "name": "Jean-Loup Dupret"
    },
    {
      "name": "Patrick Cheridito"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6hec2anwcp185.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26718",
  "fulltext_url": null,
  "id": "6hec2anwcp185",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26718",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7223026038",
  "pdf_url": "https://arxiv.org/pdf/2610.26718",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6hec2anwcp185.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:31:00Z",
      "native_id": "2610.26718",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26718"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Deep Pontryagin Learning for Continuous-Time Stochastic Control with Jumps",
  "title_text": "Deep Pontryagin Learning for Continuous-Time Stochastic Control with Jumps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:47Z",
  "url": "https://research.draconitic.com/paper/6hec2anwcp185",
  "venue": "arXiv",
  "versions": []
}