{
  "abstract": "We study how far gradient descent (GD) can be accelerated by predetermined stepsizes in smooth convex optimization. Going beyond the classical $Ω(n^{-2})$ first-order oracle lower bound of Nemirovsky and Yudin (1983), we prove an $Ω(n^{-1.6342})$ non-anytime lower bound and an $Ω(n^{-1.2408})$ anytime lower bound. These improve the recent $Ω(n^{-1.932})$ non-anytime lower bound of Ma and Chen (2026) and the $Ω(n^{-4/3})$ anytime lower bound of Tsai et al. (2026), respectively. Both results continue to hold when the stepsizes may be negative. Our anytime lower bound also shows that the $O(n^{-\\log_2(1+\\sqrt{2})})$ rate of non-anytime silver schedules (Altschuler and Parrilo, 2025; Grimmer et al., 2025) is unattainable in the anytime setting. This establishes a strict separation between the two settings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02855",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuhan Ye"
    },
    {
      "name": "Kaizhao Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8jz5pgd2vjc6r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02855",
  "fulltext_url": null,
  "id": "8jz5pgd2vjc6r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02855",
  "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": "W7207775074",
  "pdf_url": "https://arxiv.org/pdf/2609.02855",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8jz5pgd2vjc6r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.02855",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02855"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Improved Gradient Descent Lower Bounds Beyond Nesterov",
  "title_text": "Improved Gradient Descent Lower Bounds Beyond Nesterov",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:42Z",
  "url": "https://research.draconitic.com/paper/8jz5pgd2vjc6r",
  "venue": "arXiv",
  "versions": []
}