{
  "abstract": "We study second-order methods for convex stochastic optimization, where gradients and Hessians are available only through stochastic estimates with variances $σ_1^2$ and $σ_2^2$, respectively. First, we propose the Stochastic Contracting Cubic Newton method. At each iteration, it minimizes a cubic model with additional quadratic regularization and then contracts the step toward the current point. After $T$ iterations, the method achieves the expected convergence rate $\\mathcal{O}(σ_1/\\sqrt{T}+σ_2/T+1/T^2)$. Building on this construction, we develop an accelerated variant achieving $\\mathcal{O}(σ_1/\\sqrt{T}+σ_2/T^2+1/T^{7/2})$, matching the known lower bounds of Agafonov et al. (2024) in all three terms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11693",
  "author_total": 6,
  "authors": [
    {
      "name": "Artem Agafonov"
    },
    {
      "name": "Aslan Ashabokov"
    },
    {
      "name": "Dmitry Kamzolov"
    },
    {
      "name": "Alexander D'yakonov"
    },
    {
      "name": "Alexander Gasnikov"
    },
    {
      "name": "Martin Takáč"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3mf9504q4c2b0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11693",
  "fulltext_url": null,
  "id": "3mf9504q4c2b0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11693",
  "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",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7221160888",
  "pdf_url": "https://arxiv.org/pdf/2610.11693",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3mf9504q4c2b0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.11693",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11693"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Matching the Lower Bounds: Stochastic Contracting Cubic Newton and Its Optimal Acceleration",
  "title_text": "Matching the Lower Bounds: Stochastic Contracting Cubic Newton and Its Optimal Acceleration",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/3mf9504q4c2b0",
  "venue": "arXiv",
  "versions": []
}