{
  "abstract": "We study prediction with expert advice over $T$ rounds with $K$ experts under heavy-tailed losses whose $(1+ε)$-moment is bounded by $θ>0$ for some $ε\\in(0,1]$. In this setting, existing algorithms designed for the case $ε=1$ can be suboptimal when $ε<1$, suffering an additional polynomial dependence on $K$. We characterize the minimax pseudo-regret rate as $Θ((θT)^{\\frac{1}{1+ε}}(\\log K)^{\\fracε{1+ε}})$ and establish gap-dependent lower bounds in a self-bounded environment. To attain this minimax rate without prior knowledge of either $ε$ or $θ$, we propose Adaptive Heavy-Tailed FTRL, which uses robust data-dependent scale adaptation together with truncation. We further develop Adaptive Heavy-Tailed OMD, which likewise requires neither $ε$ nor $θ$ and achieves near-optimal regret guarantees in both adversarial and self-bounded environments. Finally, when $ε$ and $θ$ are known, an FTRL algorithm with Shannon-entropy regularization achieves optimal regret guarantees in both environments.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14904",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuki Shibukawa"
    },
    {
      "name": "Shinji Ito"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ckss2sg6k8nk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14904",
  "fulltext_url": null,
  "id": "1ckss2sg6k8nk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14904",
  "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": "W7221781359",
  "pdf_url": "https://arxiv.org/pdf/2610.14904",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ckss2sg6k8nk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:26Z",
      "native_id": "2610.14904",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14904"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Prediction with Expert Advice under Heavy-Tailed Losses",
  "title_text": "Prediction with Expert Advice under Heavy-Tailed Losses",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/1ckss2sg6k8nk",
  "venue": "arXiv",
  "versions": []
}