{
  "abstract": "Prediction with expert advice is a fundamental problem in online learning. When the time horizon $T$ is known in advance, the minimax cumulative regret over $n$ experts is asymptotically $\\sqrt{\\frac{T \\ln n}{2}}$. This is achieved by the Multiplicative Weights Update algorithm with a learning rate tuned to $T$, and is known to be tight. If instead the regret bound is required to hold simultaneously at every time $t$, the best known guarantee has been $\\sqrt{t \\ln n}$---a factor of $\\sqrt{2}$ worse---and it has remained unknown whether this factor of $\\sqrt{2}$ is necessary. We show that it is not. We give an algorithm, requiring no knowledge of the horizon, whose cumulative regret satisfies $R_t \\le \\bigl(1 + O(\\sqrt{\\ln \\ln n / \\ln n})\\bigr)\\sqrt{t \\ln n / 2}$ simultaneously for every $t \\ge 1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27206",
  "author_total": 7,
  "authors": [
    {
      "name": "Yang Cai"
    },
    {
      "name": "Vineet Gupta"
    },
    {
      "name": "Yanchen Jiang"
    },
    {
      "name": "Christopher Liaw"
    },
    {
      "name": "Aranyak Mehta"
    },
    {
      "name": "Grigoris Velegkas"
    },
    {
      "name": "Di Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1n9kjne07ky2x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27206",
  "fulltext_url": null,
  "id": "1n9kjne07ky2x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27206",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7214172952",
  "pdf_url": "https://arxiv.org/pdf/2609.27206",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1n9kjne07ky2x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:06Z",
      "native_id": "2609.27206",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27206"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Prediction with Expert Advice: Anytime Regret with Many Experts Matches the Fixed-Time Constant",
  "title_text": "Prediction with Expert Advice: Anytime Regret with Many Experts Matches the Fixed-Time Constant",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:06Z",
  "url": "https://research.draconitic.com/paper/1n9kjne07ky2x",
  "venue": "arXiv",
  "versions": []
}