{
  "abstract": "Worst-case Optimal Recovery (OR) and Bayesian learning describe the same Gaussian-quadratic-Hilbert problems in two vocabularies. We sharpen the correspondence - the radius of information equals a nugget-optimized GP posterior variance and is attained by the posterior mean at a closed-form balance nugget - and measure, inside three published Bayesian systems, where the worst-case side pays. The ledger is two-sided: the losses instruct as much as the wins. Morozov calibration tracks a test-access oracle within $1.00$-$1.19\\times$ where $σ$-blind rules fail, is $4.9$-$6.3\\times$ more reproducible across noise draws ($p=0.002$-$0.004$), and is the only deployable rule whose selection survives a change of backend ($1.36\\times$ against $12$-$30\\times$ for the released weight, ML-II and GCV); tight certificates cover at the information-theoretic floor with no numerical slack. But on exchangeable data split-conformal beats the OR head on interval score, a water-filling prior adds nothing without an oracle noise hint, and under covariate shift the OR band keeps coverage on every dataset yet loses interval score to split-conformal, and to a feature-free constant band, on most cells; what pays is not shift but shift on a learnable target, which a training-free audit statistic predicts before any model is fitted. In Bayesian optimization the certified width is a validity floor whose scalar inflation we prove inert under a checkable margin condition and check at every step. Inertness is graded, not binary, and in the size of the inflation as much as in the objective: $κ{=}2$ is inert wherever $κ{=}5$ is and on more cells besides, while $κ{=}5$ moves half the Ackley seeds and every Griewank seed. Exploration is a shape problem, not a scale one. The design rule: match the guarantee tool to the data regime, and audit the regime first.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29622",
  "author_total": 1,
  "authors": [
    {
      "name": "Gordei Verbii"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1d9ybv9ehqt77.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29622",
  "fulltext_url": null,
  "id": "1d9ybv9ehqt77",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29622",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Gaussian Processes and Bayesian Inference"
    ]
  ],
  "openalex": "W7214405574",
  "pdf_url": "https://arxiv.org/pdf/2609.29622",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1d9ybv9ehqt77.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:21Z",
      "native_id": "2609.29622",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29622"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Optimal Recovery Meets Bayesian Learning: Where Worst-Case Bounds Pay Off",
  "title_text": "Optimal Recovery Meets Bayesian Learning: Where Worst-Case Bounds Pay Off",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:21Z",
  "url": "https://research.draconitic.com/paper/1d9ybv9ehqt77",
  "venue": "arXiv",
  "versions": []
}