{
  "abstract": "The rate-optimal convergence rate of gradient descent (GD) with a fixed step-size is well known to be $Θ(N^{-1})$ for $L$-Lipschitz smooth convex objectives in the prior art in convex optimization. Surprisingly, several recent works show that we can accelerate vanilla GD by applying a nonconstant, nonadaptive, deterministic step-size schedule. The best-known upper bounds so far in the non-anytime & anytime setups are $O(N^{-1.271})$ [Altschuler and Parrilo, 2025, Grimmer et al., 2023] and $O(N^{-1.119})$ [Zhang et al., 2025], respectively. On the other hand, the best reported lower bounds (or barriers) up to date in the non-anytime & anytime setups are $Ω(N^{-1.635})$ and $Ω(N^{-1.241})$ [Ye and Liu, 2026], respectively. We narrow these gaps by establishing stronger lower bounds for GD's convergence rate in both settings: $Ω(N^{-1.450})$ for the non-anytime rate bound and $Ω(N^{-1.184})$ for the anytime rate barrier.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04032",
  "author_total": 3,
  "authors": [
    {
      "name": "Minchan Jung"
    },
    {
      "name": "Hanseul Cho"
    },
    {
      "name": "Chulhee Yun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cdjcfn06gwwsb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04032",
  "fulltext_url": null,
  "id": "cdjcfn06gwwsb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04032",
  "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",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7208749978",
  "pdf_url": "https://arxiv.org/pdf/2609.04032",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cdjcfn06gwwsb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04032",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04032"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Stronger Lower Bounds for (Non-)Anytime Acceleration of Gradient Descent",
  "title_text": "Stronger Lower Bounds for (Non-)Anytime Acceleration of Gradient Descent",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/cdjcfn06gwwsb",
  "venue": "arXiv",
  "versions": []
}