{
  "abstract": "Recent work demonstrated that executing Bayesian Optimization (BO) using simply a linear surrogate with a clever transformation is enough to approximate the performance of the standard Gaussian-Process (GP) based version on high-dimensional test functions. When the decision region is a sphere, this strategy admits rapid exact acquisition. However, it is the unit cube we encounter most often in the BO literature, and in this setting a standard approach, namely a multi-start quasi-Newton method, is employed for solving the acquisition subproblem. In this article, we will discuss a series of results, both positive and negative, regarding the complexity of global resolution of various acquisition subproblems over the unit cube. On the basis of this discussion, we will propose a new acquisition function which is globally optimizable using significantly less execution time than the incumbent approach while maintaining or improving performance. The resulting method is competitive with GP-based BO in terms of accuracy per evaluation, and is superior in terms of accuracy per walltime on black-boxes of low to moderate computational intensity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32628",
  "author_total": 1,
  "authors": [
    {
      "name": "Nathan Wycoff"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5eakfxz2abw6d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32628",
  "fulltext_url": null,
  "id": "5eakfxz2abw6d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32628",
  "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.CO"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7223678542",
  "pdf_url": "https://arxiv.org/pdf/2610.32628",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5eakfxz2abw6d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:25Z",
      "native_id": "2610.32628",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32628"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.CO",
      "subfield": "statistics"
    }
  ],
  "title": "Acquisition for Spherical-Linear Bayesian Optimization on the Cube",
  "title_text": "Acquisition for Spherical-Linear Bayesian Optimization on the Cube",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:25Z",
  "url": "https://research.draconitic.com/paper/5eakfxz2abw6d",
  "venue": "arXiv",
  "versions": []
}