{
  "abstract": "We study the stochastic second-order oracle complexity of solving smooth convex finite-sum optimization with $n$ components. Very recently, Tsedenov \\& Kovalev (2026) showed that the minimax optimal complexity under averaged smoothness and convexity is $\\tildeΘ(n + n^{6/7} ε^{-2/7})$ by establishing nearly matching upper and lower bounds. In this paper, we show that individual smoothness and convexity provably enable further acceleration, where the lower complexity bound is $Ω(n+ n^{5/7} ε^{-2/7})$ under this stronger assumption. Then, by establishing a novel second-order self-bounding inequality, we design a new Taylor-corrected lazy Newton method, which can lead to a better complexity of $\\tilde{\\mathcal{O}}(n + n^{5/7} ε^{-2/7})$ by applying the optimal Monteiro-Svaiter acceleration, matching our lower bound up to only logarithmic factors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.42040",
  "author_total": 4,
  "authors": [
    {
      "name": "Xinliang Zhang"
    },
    {
      "name": "Lesi Chen"
    },
    {
      "name": "Zonghan Li"
    },
    {
      "name": "Jingzhao Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fe4gdrn2c096r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.42040",
  "fulltext_url": null,
  "id": "fe4gdrn2c096r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.42040",
  "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.AI"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "stat.ML"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.42040",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fe4gdrn2c096r.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.42040",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.42040"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Near-Optimal Second-Order Convex Finite-Sum Optimization under Individual Smoothness",
  "title_text": "Near-Optimal Second-Order Convex Finite-Sum Optimization under Individual Smoothness",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/fe4gdrn2c096r",
  "venue": "arXiv",
  "versions": []
}