{
  "abstract": "We consider an infinite-horizon discounted dynamic programming (DP) problem for a countable-innovation belief-state model. The model is a surrogate for a linear-Gaussian dual control problem involving an unknown parameter vector and Gaussian observation noise. The surrogate preserves the first two moments of the Gaussian innovation and the resulting posterior second-moment structure. We allow unbounded belief and control spaces and nonnegative stage costs with quadratic growth in the posterior mean and covariance. Using a posterior-moment weight, we show that the Bellman operator is a contraction in a weighted sup-norm space. We characterize the optimal cost as the unique solution of the Bellman equation in this space, establish the existence of optimal stationary policies. We further prove weighted sup-norm convergence of value iteration, policy iteration, and optimistic policy iteration under vanishing approximation errors. The convergence results under vanishing approximation errors rely on general weighted sup-norm contraction properties and are applicable beyond the particular dual control problem considered here.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18630",
  "author_total": 3,
  "authors": [
    {
      "name": "Ying Wang"
    },
    {
      "name": "Yuchao Li"
    },
    {
      "name": "Håkan Hjalmarsson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aw1kfps1hhrv3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18630",
  "fulltext_url": null,
  "id": "aw1kfps1hhrv3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18630",
  "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",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Adaptive Dynamic Programming Control"
    ]
  ],
  "openalex": "W7221813538",
  "pdf_url": "https://arxiv.org/pdf/2610.18630",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aw1kfps1hhrv3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18630",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18630"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Dynamic Programming for A Linear-Gaussian Dual Control Problem",
  "title_text": "Dynamic Programming for A Linear-Gaussian Dual Control Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/aw1kfps1hhrv3",
  "venue": "arXiv",
  "versions": []
}