{
  "abstract": "We develop a regression-based Monte Carlo framework for stochastic impulse control problems with controls taking values in a compact set. The method combines dynamic programming over discrete intervention times, neural networks to estimate continuation values, and a randomized search to select interventions. We first establish a time-discretization result for δ-separated strategies, proving an approximation error of order O(h^1/2 ), with h the mesh of the discretization. On the discrete grid, we derive a dynamic programming representation of the solution in terms of intervention regions and iteratively defined stopping rules, together with a verification lemma characterizing optimal strategies. Building on this representation, we introduce a backward numerical algorithm in the spirit of regression Monte Carlo methods, and extend it to controllers constrained to a finite intervention budget. For piecewise affine intervention objectives, we derive a direct geometric bound on the error introduced by the randomized selection step. Numerical experiments on classical dividend-distribution and harvesting problems are reported in dimensions up to six. In the reported out-of-sample policy comparisons in dimensions one and six, the learned policies outperform the grid-restricted stationary band benchmark under the corresponding finite-horizon criteria.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 5,
  "authors": [
    {
      "name": "Lokman Abbas-Turki"
    },
    {
      "name": "Aurélien Grenard"
    },
    {
      "name": "Idris Kharroubi"
    },
    {
      "name": "Qinghua Li"
    },
    {
      "name": "Antonio Ocello"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dkez48vkgq0wk.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "dkez48vkgq0wk",
  "issns": [],
  "landing_url": "https://hal.science/hal-05773012v1",
  "language": "en",
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05773012/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dkez48vkgq0wk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:45Z",
      "native_id": "hal-05773012",
      "source": "hal",
      "url": "https://hal.science/hal-05773012v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "Neural Regression and Randomized Optimization for Impulse Control",
  "title_text": "Neural Regression and Randomized Optimization for Impulse Control",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:45Z",
  "url": "https://research.draconitic.com/paper/dkez48vkgq0wk",
  "venue": "HAL",
  "versions": []
}