{
  "abstract": "We study functional bilevel optimization with conditional moments, where plug-in hypergradients can inherit first-order errors from nonparametrically learned conditional expectations. We introduce OBiGrad, an orthogonalized hypergradient estimator whose bias is a product of nuisance errors. Under our regression and complexity conditions, projected gradient descent with the direct plug-in hypergradient yields expected stationarity error $O(T^{-1/2}+n^{-1/2}+n^{-ν/b})$ for the best iterate, whereas OBiGrad achieves $O(T^{-1/2}+n^{-1/2}+n^{-2ν/b})$, where $b=ν(2+p)+γ$ combines the approximation and complexity exponents. Consequently, when $ν(2-p)\\geγ$, OBiGrad attains the parametric statistical rate $O(T^{-1/2}+n^{-1/2})$, improving the sufficient sample-size bound relative to the direct plug-in bound for a fixed iteration budget. We illustrate these gains on instrumental-variable and fitted-Q-regression problems, examining stationary-point estimation, returned population stationarity, and regularization sensitivity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.21341",
  "author_total": 5,
  "authors": [
    {
      "name": "Fares El Khoury"
    },
    {
      "name": "Houssam Zenati"
    },
    {
      "name": "Nathan Kallus"
    },
    {
      "name": "Michael Arbel"
    },
    {
      "name": "Aurélien Bibaut"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/baqr6ytdwx2t2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.21341",
  "fulltext_url": null,
  "id": "baqr6ytdwx2t2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.21341",
  "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|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7161955451",
  "pdf_url": "https://arxiv.org/pdf/2605.21341",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/baqr6ytdwx2t2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:59Z",
      "native_id": "2605.21341",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.21341"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Parametric Rates for Nonparametric Conditional-Moment Bilevel Optimization",
  "title_text": "Parametric Rates for Nonparametric Conditional-Moment Bilevel Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:59Z",
  "url": "https://research.draconitic.com/paper/baqr6ytdwx2t2",
  "venue": "arXiv",
  "versions": []
}