{
  "abstract": "This work considers projection-free online learning algorithms with linear minimization oracles for handling the decision set. For Online Frank--Wolfe (OFW), regret upper bounds were already known for specific OFW tunings [Hazan and Kale, 2012, Hazan, 2016] which scaled as $T^{3/4}$ (where $T$ is the horizon length). However, it remained an open question whether the regret of all OFW tunings scaled as $T^{3/4}$. We answer that question, proving a universal worst-case regret lower bound $Ω(T^{3/4} m^{-1/4})$ for any projection-free algorithm that makes at most $m$ linear minimization oracle calls per round. The analysis suggests an extended OFW to resort to multiple linear optimizations per round, for which we prove a regret upper bound $O(\\max \\{ T^{3/4} m^{-1/4}, \\sqrt{T} \\})$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37845",
  "author_total": 4,
  "authors": [
    {
      "name": "Julien Weibel"
    },
    {
      "name": "Pierre Gaillard"
    },
    {
      "name": "Wouter Koolen"
    },
    {
      "name": "Adrien Taylor"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/80gzp23z5xsgm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37845",
  "fulltext_url": null,
  "id": "80gzp23z5xsgm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37845",
  "language": "en",
  "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": [
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      "arxiv",
      "cs.LG"
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      "arxiv",
      "stat.ML"
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.37845",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/80gzp23z5xsgm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:41Z",
      "native_id": "2610.37845",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37845"
    },
    {
      "first_seen": "2026-10-31T12:20:56Z",
      "native_id": "hal-05845829",
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      "url": "https://hal.science/hal-05845829v1"
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  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "An $Ω(T^{3/4})$ lower bound for projection-free online learning with linear minimization oracles",
  "title_text": "An Ω(T^3/4) lower bound for projection-free online learning with linear minimization oracles",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:00Z",
  "url": "https://research.draconitic.com/paper/80gzp23z5xsgm",
  "venue": "arXiv",
  "versions": []
}