{
  "abstract": "Chambolle-Dossal acceleration guarantees $F(x_n)-F^*=o(n^{-2})$ for every fixed smooth convex loss with a minimizer. We show that this qualitative improvement admits no universal quantitative rate. For every damping parameter $α>3$ and positive nondecreasing gain $G(n)\\to\\infty$, we construct a fixed one-dimensional smooth convex loss whose exact CD orbit satisfies $\\sup_{n\\ge1} n^2G(n)\\bigl(F(x_n)-F^*\\bigr)=\\infty$. Thus no divergent gain improves the $n^{-2}$ scale for all fixed losses, even with instance-dependent constants. The construction prescribes queried gradients and realizes infinitely many slow blocks within one smooth convex objective. Under local $p$-power growth with $p>2$ and sufficiently strong damping, we also construct a fixed loss whose exact CD orbit satisfies $F(x_n)-F^*\\sim Dn^{-2p/(p-2)}$, $D>0$, establishing the sharpness of the known convergence rate. Both main results are formally verified in Lean 4.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31557",
  "author_total": 6,
  "authors": [
    {
      "name": "Yuchen Yang"
    },
    {
      "name": "Xinan Dai"
    },
    {
      "name": "Wenhao Deng"
    },
    {
      "name": "Yingdong Shi"
    },
    {
      "name": "Feng Xu"
    },
    {
      "name": "Tailin Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dpgaajtbhpyb0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31557",
  "fulltext_url": null,
  "id": "dpgaajtbhpyb0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31557",
  "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": "W7214637766",
  "pdf_url": "https://arxiv.org/pdf/2609.31557",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dpgaajtbhpyb0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31557",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31557"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "No Universal Remainder Rate for Chambolle-Dossal Acceleration",
  "title_text": "No Universal Remainder Rate for Chambolle-Dossal Acceleration",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/dpgaajtbhpyb0",
  "venue": "arXiv",
  "versions": []
}