{
  "abstract": "We investigate stochastic simple bilevel optimization with smooth and possibly nonconvex upper- and lower-level objectives. Existing stochastic extensions of dynamic barrier gradient descent (DBGD) either obtain fast convergence under an unverifiable trajectory-dependent ``rare-visit'' assumption, or remove this assumption at a substantially higher oracle cost. We show that a simple denominator-only regularization of the DBGD multiplier eliminates the need for such an assumption while preserving fast convergence rates. Specifically, our method achieves $(\\varepsilon, \\varepsilon)$-stationarity in $O(\\varepsilon^{-2})$ iterations using $O(\\varepsilon^{-4})$ upper-level and $O(\\varepsilon^{-7})$ lower-level stochastic gradients, which improves upon the best assumption-free complexities. We additionally derive anytime parameter schedules.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06580",
  "author_total": 4,
  "authors": [
    {
      "name": "Daniel Cortild"
    },
    {
      "name": "Mathias Staudigl"
    },
    {
      "name": "Juan Peypouquet"
    },
    {
      "name": "Coralia Cartis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3n9543nr53cj1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06580",
  "fulltext_url": null,
  "id": "3n9543nr53cj1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06580",
  "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",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7212087685",
  "pdf_url": "https://arxiv.org/pdf/2609.06580",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3n9543nr53cj1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06580",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06580"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Stochastic Nonconvex Bilevel Optimization: Improved Rates Without Rare-Visit Assumption",
  "title_text": "Stochastic Nonconvex Bilevel Optimization: Improved Rates Without Rare-Visit Assumption",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/3n9543nr53cj1",
  "venue": "arXiv",
  "versions": []
}