{
  "abstract": "We analyze a neural semi-discrete method for high-dimensional first-order Hamilton-Jacobi-Bellman (HJB) equations with known or learned dynamics. Centered differences and an artificial viscosity $Nh=O(h)$ define a monotone operator evaluated through $2d+1$ shifted network queries; policy iteration solves the resulting Bellman equation without a tensor grid. At fixed $h$, the sharp componentwise condition $\\max_i|f_i|\\le2N$ turns every frozen-policy operator into a nearest-neighbor Markov-chain generator with a policy-independent total jump rate. Uniformization gives whole-space well-posedness for measurable feedbacks, an explicit Poisson-tail bound on the numerical domain of dependence, and boundary-free localization. The representation also yields a posteriori policy-evaluation bounds that account for residual and learned-model errors. A greedy-gap analysis controls inexact policy iteration at fixed $h$; a separate consistency estimate connects the semi-discrete equation to the continuous HJB equation. Experiments reproduce the extremal tail, show rates consistent with $O(\\sqrt h)$ and nearly $h$-independent exact-policy-iteration decay, and assess empirical estimator effectivity. A nonsmooth example shows that the continuous residual can miss a non-viscosity solution, whereas the shifted residual detects the defect. Further tests provide a structured interval-verified certificate calibration, an early-budget benefit of policy freezing for bang-bang control, and learned-dynamics diagnostics. A structured nonlinear problem with active compact-control constraints is tested against a manufactured semi-discrete reference through $d=1024$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.07116",
  "author_total": 4,
  "authors": [
    {
      "name": "Minseok Kim"
    },
    {
      "name": "Yeongjong Kim"
    },
    {
      "name": "Namkyeong Cho"
    },
    {
      "name": "Yeoneung Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9pb1zr0mac2q5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.07116",
  "fulltext_url": null,
  "id": "9pb1zr0mac2q5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.07116",
  "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.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Adaptive Dynamic Programming Control"
    ]
  ],
  "openalex": "W7160839656",
  "pdf_url": "https://arxiv.org/pdf/2605.07116",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9pb1zr0mac2q5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2605.07116",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.07116"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Monotone Neural Policy Iteration for High-Dimensional First-Order Hamilton--Jacobi--Bellman Equations",
  "title_text": "Monotone Neural Policy Iteration for High-Dimensional First-Order Hamilton--Jacobi--Bellman Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/9pb1zr0mac2q5",
  "venue": "arXiv",
  "versions": []
}