{
  "abstract": "In high-dimensional dynamic treatment regimes, nonlinear terminal outcome models complicate upstream conditional-mean modeling and inference based on recursively estimated continuation values. We introduce a Deformed Q-learning procedure for general action spaces that accommodates a terminal-stage GLM, random designs, conditional heteroscedasticity, and fine-grained action discretization. The procedure changes the recursive criterion by propagating the terminal deformed optimal Q-function through sparse block-wise linear conditional-mean models. Under the stated models and regularity conditions, we establish consistent and asymptotically normal estimators, accounting for downstream estimation uncertainty in inference for optimal Q-values, deformed optimal Q-values, and their contrasts. We bound population regret relative to the original terminal mean-outcome objective without explicit stage-wise accumulation. Estimation and inference also extend to a growing number of stages under conditions uniform across stages. Simulation studies demonstrate accurate estimation and variable selection. In an empirical application to sepsis management using the MIMIC-III database, the proposed framework supports stage-specific value inference, while an auxiliary action-alignment analysis provides an exploratory signal that early-stage concordance with the learned recommendation may be associated with improved survival.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00929",
  "author_total": 3,
  "authors": [
    {
      "name": "Ming Cheng"
    },
    {
      "name": "Zhao Chen"
    },
    {
      "name": "Christina Dan Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/297qfst3ewcz7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00929",
  "fulltext_url": null,
  "id": "297qfst3ewcz7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00929",
  "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.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00929",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/297qfst3ewcz7.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00929",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00929"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Deformed Q-learning for High-Dimensional Dynamic Treatment Regimes",
  "title_text": "Deformed Q-learning for High-Dimensional Dynamic Treatment Regimes",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:35Z",
  "url": "https://research.draconitic.com/paper/297qfst3ewcz7",
  "venue": "arXiv",
  "versions": []
}