{
  "abstract": "Continuous-time reinforcement learning seeks an optimal policy under unknown dynamics driven by stochastic differential equations using observations collected at discrete times. We develop a policy gradient framework that combines rigorous convergence analysis with learning from discrete data. We first establish a performance difference lemma and derive policy gradient formulas for randomized and parametrized policies. We then prove exponential convergence of an entropy-regularized policy flow to the regularized optimum. For discrete parametrized updates, we derive a convergence bound that explicitly separates the contributions of critic error, policy-regression error, and the learning step size. To enable learning under unknown dynamics, we integrate this framework with PhiBE, which constructs a continuous-time surrogate generator from discrete transition data. The resulting on-policy and off-policy model-free actor-critic algorithms preserve the continuous-time structure of the control problem. Numerical experiments on an entropy-regularized linear-quadratic regulator and a nonlinear wheeled robot demonstrate the performance and stability of the proposed methods with both known and data-driven dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28580",
  "author_total": 4,
  "authors": [
    {
      "name": "Martin Hernandez"
    },
    {
      "name": "Xinyan Qing"
    },
    {
      "name": "Mo Zhou"
    },
    {
      "name": "Yuhua Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2affkynsxsfr5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28580",
  "fulltext_url": null,
  "id": "2affkynsxsfr5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28580",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Reinforcement Learning in Robotics"
    ]
  ],
  "openalex": "W7223127268",
  "pdf_url": "https://arxiv.org/pdf/2610.28580",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2affkynsxsfr5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28580",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28580"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Continuous-Time Policy Gradient from Discrete Data: Convergence Analysis and Model-Free Algorithms",
  "title_text": "Continuous-Time Policy Gradient from Discrete Data: Convergence Analysis and Model-Free Algorithms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/2affkynsxsfr5",
  "venue": "arXiv",
  "versions": []
}