{
  "abstract": "We study quantum multi-armed bandits (QMAB) and quantum linear bandits (QLB), where the learner queries each arm or action through a quantum reward oracle or its inverse. Prior work gives algorithms over horizon $T$ with regret $O(K\\log T)$ for QMAB with $K$ arms and $O(d^2\\operatorname{polylog} T)$ for $d$-dimensional QLB. This leaves open the optimal dependence on $K$ and $T$ and whether the dependence on $d$ can be further improved. In this work, we prove the first tight minimax regret bound of $Θ(K\\log(1+T/K))$ for QMAB and the first lower bound of $Ω(d\\log(1+T/d))$ for finite-action QLB, ruling out regret independent of $T$. Our lower bounds rely on a high-confidence single-arm quantum testing lower bound for distinguishing a fixed reward mean from an interval of alternatives. A bandit-to-testing reduction then lifts it to the QMAB lower bound, while a linear embedding gives the finite-action QLB lower bound. The matching QMAB upper bound is obtained using a tail bound for the Quantum Monte Carlo (QMC) estimator. For finite-action QLB, we propose a phased elimination algorithm that combines a low-bias low-variance quantum mean estimator with a small-support $G$-optimal design through a query allocation matched to the design weights. When the action set has size $\\operatorname{poly}(d)$, its regret is nearly linear in $d$ and matches our lower bound up to polylogarithmic factors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.14319",
  "author_total": 3,
  "authors": [
    {
      "name": "Maoli Liu"
    },
    {
      "name": "Zhuohua Li"
    },
    {
      "name": "John C. S. Lui"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ea1xgdrsd1n37.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.14319",
  "fulltext_url": null,
  "id": "ea1xgdrsd1n37",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.14319",
  "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.LG"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7203636633",
  "pdf_url": "https://arxiv.org/pdf/2608.14319",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ea1xgdrsd1n37.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2608.14319",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.14319"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum Multi-Armed Bandits and Linear Bandits: Lower Bounds and Algorithms",
  "title_text": "Quantum Multi-Armed Bandits and Linear Bandits: Lower Bounds and Algorithms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:54Z",
  "url": "https://research.draconitic.com/paper/ea1xgdrsd1n37",
  "venue": "arXiv",
  "versions": []
}