{
  "abstract": "Best arm identification under differential privacy is a pure-exploration problem in which both statistical efficiency and privacy protection must be achieved simultaneously. We study fixed-budget best arm identification for bandits under pure $ε$-differential privacy, where the learner must recommend an arm after a prescribed sampling budget while protecting the full transcript. We prove that the optimal exponential decay rate of the error probability is upper bounded by an instance-dependent privacy-aware transportation exponent that differs from the analogous quantity used to characterize the stopping time in fixed-confidence analysis by Jourdan and Azize [2025]. Guided by this exponent, we propose AO-Pri-BAI, an adaptive algorithm that maintains private running estimates through Laplace-tree mechanisms and learns a sampling design through a min--max interaction between hard alternatives and arm allocations. We prove that AO-Pri-BAI satisfies pure $ε$-differential privacy. We also establish that the exponent of the failure probability of AO-Pri-BAI matches the privacy-aware benchmark. Numerical studies show that even in the non-asymptotic setting, AO-Pri-BAI outperforms benchmark algorithms on various instances, complementing the theoretical analyses.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04600",
  "author_total": 4,
  "authors": [
    {
      "name": "Keqin Chen"
    },
    {
      "name": "Jie Bian"
    },
    {
      "name": "Yulian Wu"
    },
    {
      "name": "Vincent Y. F. Tan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f7emmb3s48njp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04600",
  "fulltext_url": null,
  "id": "f7emmb3s48njp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04600",
  "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.IT"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7220660067",
  "pdf_url": "https://arxiv.org/pdf/2610.04600",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f7emmb3s48njp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.04600",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04600"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Asymptotically Optimal Best Arm Identification with Fixed-Budget under Differential Privacy",
  "title_text": "Asymptotically Optimal Best Arm Identification with Fixed-Budget under Differential Privacy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/f7emmb3s48njp",
  "venue": "arXiv",
  "versions": []
}