{
  "abstract": "Bilevel optimization provides a framework for machine learning tasks such as hyperparameter optimization, data reweighting, and meta-learning. Existing Newton-based bilevel methods typically rely on the classical hypergradient formula, which is generally unavailable when lower-level solutions are nonunique and the lower-level Hessian is singular. We develop two Newton-based methods beyond lower-level strong convexity by exploiting curvature shared by the lower-level and multiplier updates. Newton-based GALET handles potentially singular lower-level curvature under a positive spectral-gap condition, exploiting its range structure to avoid the squared-Hessian multiplier system used in GALET. Newton-based BAMM uses a strongly convex aggregation model when the lower-level objective is convex and the upper-level objective is strongly convex in the lower-level variable. We establish convergence guarantees and improved complexity bounds relative to GALET and sl-BAMM under the corresponding assumptions. We further introduce GNBO, a generalized Newton-based framework that captures the shared-curvature structure of the proposed methods and several existing Newton and quasi-Newton bilevel methods. Experiments on synthetic problems, data hyper-cleaning, and GPT-2 data reweighting evaluate the proposed methods across different bilevel learning tasks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26839",
  "author_total": 4,
  "authors": [
    {
      "name": "Youran Dong"
    },
    {
      "name": "Junfeng Yang"
    },
    {
      "name": "Wei Yao"
    },
    {
      "name": "Jin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0easda73vvhd0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26839",
  "fulltext_url": null,
  "id": "0easda73vvhd0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26839",
  "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.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7223026638",
  "pdf_url": "https://arxiv.org/pdf/2610.26839",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0easda73vvhd0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:31:00Z",
      "native_id": "2610.26839",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26839"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Newton-Based Methods for Bilevel Optimization Beyond Lower-Level Strong Convexity",
  "title_text": "Newton-Based Methods for Bilevel Optimization Beyond Lower-Level Strong Convexity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:47Z",
  "url": "https://research.draconitic.com/paper/0easda73vvhd0",
  "venue": "arXiv",
  "versions": []
}