{
  "abstract": "We study multi-armed bandits (MAB) with multiple optimal arms, motivated by the fact that many practical decision making problems admit multiple correct answers. For $K$-armed bandits with $A$ optimal arms, we first provide a sharper analysis of previous sub-sampling algorithms (De Heide et al., 2021; Zhu and Nowak, 2020), establishing a $\\tilde{O}\\Big(\\frac{K-A}{\\sqrt{KA}}\\sqrt{T} \\Big)$ minimax regret, where $T$ is the total number of interactions and $\\tilde O(\\cdot)$ drops all constant and logarithmic factors, improving the previous $\\tilde{O}(\\sqrt{KT/A})$ regret. We then provide a matching lower bound up to logarithmic factors, indicating that our established rate is nearly minimax-optimal. We further show that the knowledge of $A$ up to $\\tilde{O}(1)$ factors is necessary to achieve near-optimal regret, as near-optimal algorithms for one number of optimal arms must incur substantially larger regret than optimal regret for a smaller number. Overall, our results provide a comprehensive minimax characterization of $K$-armed bandits with $A$ over the entire range of $1 \\leq A \\leq K-1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38659",
  "author_total": 5,
  "authors": [
    {
      "name": "Kaixuan Ji"
    },
    {
      "name": "Qiwei Di"
    },
    {
      "name": "Qingyue Zhao"
    },
    {
      "name": "Heyang Zhao"
    },
    {
      "name": "Quanquan Gu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5ptbwk4maf55z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38659",
  "fulltext_url": null,
  "id": "5ptbwk4maf55z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38659",
  "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.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7215126984",
  "pdf_url": "https://arxiv.org/pdf/2609.38659",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5ptbwk4maf55z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2609.38659",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38659"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Bandits with Multiple Optimal Arms: Minimax Regret and Non-Adaptivity",
  "title_text": "Bandits with Multiple Optimal Arms: Minimax Regret and Non-Adaptivity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:14Z",
  "url": "https://research.draconitic.com/paper/5ptbwk4maf55z",
  "venue": "arXiv",
  "versions": []
}