{
  "abstract": "We study fixed-confidence best-arm identification under strict 1-bit feedback constraints. At each round, the learner selects an arm and a query set, and receives only a single bit indicating whether the sampled reward belongs to that set. We consider a distribution-free finite-variance setting with arm-wise localization, where direct empirical mean estimation is no longer available and clipping becomes unavoidable. We first formulate a time-uniform 1-bit mean-estimation primitive based on randomized threshold queries and a clipped tail-integral identity. We then embed this primitive into candidate-challenger best-arm identification algorithms. A fixed-clipping algorithm gives a simple anytime $(ε,δ)$-PAC guarantee, while a phased adaptive-clipping algorithm matches the clipping level to the current resolution and yields a gap-adaptive sample complexity. We also prove a $K$-arm worst-case information-theoretic lower bound showing that the logarithmic penalty caused by finite-variance 1-bit feedback is intrinsic. This bound matches the leading dependence of the phased algorithm up to lower-order $\\log\\log$ factors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02771",
  "author_total": 5,
  "authors": [
    {
      "name": "Khang Luong"
    },
    {
      "name": "Dinh Thai Son"
    },
    {
      "name": "Hoang Ta"
    },
    {
      "name": "Hung The Tran"
    },
    {
      "name": "Tuan Quang Dam"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/azk375pmsz5ef.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02771",
  "fulltext_url": null,
  "id": "azk375pmsz5ef",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02771",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7220441212",
  "pdf_url": "https://arxiv.org/pdf/2610.02771",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/azk375pmsz5ef.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:56Z",
      "native_id": "2610.02771",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02771"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Nearly Optimal Fixed-Confidence Best-Arm Identification with 1-Bit Feedback",
  "title_text": "Nearly Optimal Fixed-Confidence Best-Arm Identification with 1-Bit Feedback",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:56Z",
  "url": "https://research.draconitic.com/paper/azk375pmsz5ef",
  "venue": "arXiv",
  "versions": []
}