{
  "abstract": "We determine the optimal regret in agnostic multiclass online learning with arbitrary, possibly infinite, label spaces. For every hypothesis class of multiclass Littlestone dimension $d<\\infty$, we prove a regret upper bound of $O(\\min\\{T,\\sqrt{dT}\\})$ over $T$ rounds, matching the known lower bound. This resolves a question of Hanneke et al. (2023) and extends the optimal binary regret bound of Alon et al. (2021). Our proof strengthens the one-sided expert cover of Hanneke et al. (2023) to a fractional cover. We combine this cover with a minimax reduction to a finite expert game, whose best-response rewards provide the disagreement bounds needed for chaining.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32339",
  "author_total": 2,
  "authors": [
    {
      "name": "Sajad Ashkezari"
    },
    {
      "name": "Shai Ben-David"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/288jx5d2148wd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32339",
  "fulltext_url": null,
  "id": "288jx5d2148wd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32339",
  "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",
      "stat.ML"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7223650774",
  "pdf_url": "https://arxiv.org/pdf/2610.32339",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/288jx5d2148wd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:25Z",
      "native_id": "2610.32339",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32339"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Optimal Multiclass Online Regret with Arbitrary Label Spaces",
  "title_text": "Optimal Multiclass Online Regret with Arbitrary Label Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:25Z",
  "url": "https://research.draconitic.com/paper/288jx5d2148wd",
  "venue": "arXiv",
  "versions": []
}