{
  "abstract": "Efficient global optimization aims to identify a global optimum of an expensive black-box function within a limited evaluation budget $N$. We investigate the convergence rates of Gaussian process Thompson sampling (GP-TS) under noiseless observations, assuming a fixed objective function in a reproducing kernel Hilbert space (RKHS). For Matérn kernels with smoothness parameter $ν$ in dimension $d$, we establish a worst-case expected simple-regret upper bound of $O(N^{-ν/d}\\sqrt{\\log N})$ for both discrete GP-TS on sufficiently fine grids and its continuous counterpart. For the continuous implementation, we develop a nested-grid argument to control posterior sample paths over the entire domain. We further establish matching lower bounds of $Ω(N^{-5/2}\\sqrt{\\log N})$ for both implementations under a fixed one-dimensional Matérn-$5/2$ kernel, demonstrating that the logarithmic penalty is intrinsic to standard GP-TS in this setting. Motivated by this limitation, we propose Gaussian Process Capped Thompson Sampling (GP-CTS), which caps posterior sample paths using a valid RKHS norm upper bound while preserving optimism. This modification successfully eliminates the logarithmic penalty and achieves the minimax-optimal rate $Θ(N^{-ν/d})$ for both discrete and continuous implementations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19925",
  "author_total": 2,
  "authors": [
    {
      "name": "Haowei Wang"
    },
    {
      "name": "Yilin Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1wf1kr4wcwf6w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19925",
  "fulltext_url": null,
  "id": "1wf1kr4wcwf6w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19925",
  "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",
      "stat.ML"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7221953227",
  "pdf_url": "https://arxiv.org/pdf/2610.19925",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1wf1kr4wcwf6w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:42Z",
      "native_id": "2610.19925",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19925"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Convergence Rates of Gaussian Process Thompson Sampling for Efficient Global Optimization",
  "title_text": "Convergence Rates of Gaussian Process Thompson Sampling for Efficient Global Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:42Z",
  "url": "https://research.draconitic.com/paper/1wf1kr4wcwf6w",
  "venue": "arXiv",
  "versions": []
}