{
  "abstract": "We study policy evaluation (PE) and policy gradient (PG) for continuous-time stochastic control with Markov regime-switching. The main challenges are the coexistence of diffusion and regime jumps, the coupling of regime-dependent value functions, and the construction of model-free learning rules from the coupled generators. We establish a martingale characterization of PE that incorporates both Brownian and switching martingales, and extend martingale loss and orthogonality methods to this setting. We further derive a coupled PG equation and a trajectory-based gradient representation that, under an action-independent switching generator, avoids explicit knowledge of the system coefficients and transition rates. These results lead to offline and online actor-critic algorithms. We also establish convergence and study the finite-grid approximation required for implementation. Numerical experiments for a regime-switching linear-quadratic problem illustrate the proposed methods.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31094",
  "author_total": 3,
  "authors": [
    {
      "name": "Minghui Zhang"
    },
    {
      "name": "Xun Li"
    },
    {
      "name": "Xin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3gncvje0n8a7q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31094",
  "fulltext_url": null,
  "id": "3gncvje0n8a7q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31094",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Adaptive Dynamic Programming Control"
    ]
  ],
  "openalex": "W7223408297",
  "pdf_url": "https://arxiv.org/pdf/2610.31094",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3gncvje0n8a7q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31094",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31094"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Policy Evaluation and Policy Gradient for Continuous-Time Markov Regime-Switching Systems",
  "title_text": "Policy Evaluation and Policy Gradient for Continuous-Time Markov Regime-Switching Systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/3gncvje0n8a7q",
  "venue": "arXiv",
  "versions": []
}