{
  "abstract": "Calibrated multiaccuracy asks that a predictor be globally calibrated and multiaccurate with respect to a bounded test family $G$; that is, its residuals should be uncorrelated with every test $g(x)\\in G$. This weakening of multicalibration suffices for many applications. Its sample complexity was not known to improve on that of full multicalibration, which is $\\widetildeΘ\\left(\\frac{\\log|G|}{\\varepsilon^2} + \\frac{1}{\\varepsilon^{3}}\\right)$ when $|G|$ is at least a sufficiently large power of $\\log(1/\\varepsilon)$. We resolve the sample complexity of $\\varepsilon$-calibrated multiaccuracy, showing that it scales as $$ \\widetildeΘ\\left(\\frac{\\log|G|}{\\varepsilon^2} + \\frac{1}{\\varepsilon^{5/2}}\\right), $$ separating it from the complexity of multicalibration. The upper bound is obtained by an algorithm that outputs a randomized predictor. For deterministic predictors, we establish the tight rate $$ \\widetildeΘ\\left( \\frac{\\log|G|}{\\varepsilon^2} + \\frac{(\\log|G|)^{1/3}}{\\varepsilon^{8/3}} \\right) $$ whenever $\\log|G|=Ω(\\log(1/\\varepsilon))$. When $\\log|G|\\le\\varepsilon^{-1+κ}$ for any fixed $κ\\in(0,1)$, this rate is polynomially larger than the rate for randomized predictors. Thus, unlike for multicalibration, calibrated multiaccuracy exhibits a genuine sample-complexity separation between deterministic and randomized predictors. The matching upper and lower bounds show that the unusual cube-root dependence on $\\log|G|$ is intrinsic. At $\\log|G|\\asymp\\varepsilon^{-1}$, the minimax rates for randomized and deterministic calibrated multiaccuracy both coincide with the minimax rate for multicalibration.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03305",
  "author_total": 3,
  "authors": [
    {
      "name": "Jiuyao Lu"
    },
    {
      "name": "Georgy Noarov"
    },
    {
      "name": "Aaron Roth"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2jsnfn87v0b5z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03305",
  "fulltext_url": null,
  "id": "2jsnfn87v0b5z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03305",
  "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.DS"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03305",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2jsnfn87v0b5z.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03305",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03305"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Calibrated Multiaccuracy: Deterministic and Randomized Sample Complexity",
  "title_text": "Calibrated Multiaccuracy: Deterministic and Randomized Sample Complexity",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:35Z",
  "url": "https://research.draconitic.com/paper/2jsnfn87v0b5z",
  "venue": "arXiv",
  "versions": []
}