{
  "abstract": "We study nonconvex--strongly-convex bilevel optimization with finite-sum objectives and fully first-order oracles. We propose Sampled Implicit Corrections for Bilevel Optimization (SICBO), which combines a penalty approximation with variance-reduced corrections for the lower-level variables. Under componentwise lower strong convexity, SICBO finds a point $x$ satisfying $\\mathbb{E}\\|\\nablaΦ(x)\\|^2\\le\\varepsilon^2$ within $\\tilde{O}(N+\\sqrt{N}κ^{7/2}\\varepsilon^{-2})$ component-gradient calls, where $N$ is the total number of components and $κ$ is the normalized lower-level condition number. The bound achieves square-root finite-sum dependence using only gradients and preserves the best known deterministic fully first-order condition-number exponent for smooth problems. Our improvement follows from a curvature-dependent bound for nonlinear correction errors, which permits epochs of length $\\tildeΘ(\\sqrt{N/κ})$ with batches of size $\\tildeΘ(\\sqrt{Nκ})$. A single-level reduction shows that the dependence on $N$ and $\\varepsilon$ is optimal up to logarithmic factors for fixed $κ$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24538",
  "author_total": 2,
  "authors": [
    {
      "name": "Qihao Zhou"
    },
    {
      "name": "Shanshui Niu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ektgra4z7fb8x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24538",
  "fulltext_url": null,
  "id": "ektgra4z7fb8x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24538",
  "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"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7223016097",
  "pdf_url": "https://arxiv.org/pdf/2610.24538",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ektgra4z7fb8x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24538",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24538"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Accelerating Finite-Sum Bilevel Optimization with Fully First-Order Oracles",
  "title_text": "Accelerating Finite-Sum Bilevel Optimization with Fully First-Order Oracles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:54Z",
  "url": "https://research.draconitic.com/paper/ektgra4z7fb8x",
  "venue": "arXiv",
  "versions": []
}