{
  "abstract": "We give a proper membership-query algorithm for agnostically learning halfspaces under the uniform distribution on $\\{\\pm1\\}^n$. Given query access to an arbitrary function $f:\\{\\pm1\\}^n \\to \\{\\pm1\\}$, our algorithm runs in time $\\mathrm{poly}(n)+2^{\\mathrm{poly}(1/\\varepsilon)}$ and outputs a halfspace with error at most $\\mathrm{OPT}+\\varepsilon$, where $\\mathrm{OPT}$ is the error of the best-fitting halfspace for $f$. Previously, even with membership queries, the best known running time was $n^{\\mathrm{poly}(1/\\varepsilon)}$, achieved by the sample-based algorithm of Kalai, Klivans, Mansour, and Servedio (FOCS 2005). Our algorithm is the first agnostic halfspace learner under the uniform distribution on $\\{\\pm1\\}^n$ whose running time is polynomial in $n$ with an exponent independent of $\\varepsilon$. Combining our algorithm with a boosting argument yields a proper agnostic learner using only random examples. It achieves the same $\\mathrm{OPT}+\\varepsilon$ guarantee, with running time matching that of Kalai et al.\\ up to an additive term depending only on $\\varepsilon$. To our knowledge, this is the first sample-based proper agnostic learner in the Boolean setting with running time $2^{o(n)}$ for every fixed $\\varepsilon>0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02344",
  "author_total": 4,
  "authors": [
    {
      "name": "Anindya De"
    },
    {
      "name": "Elchanan Mossel"
    },
    {
      "name": "Shivam Nadimpalli"
    },
    {
      "name": "Joe Neeman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8tzn25045k6xf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02344",
  "fulltext_url": null,
  "id": "8tzn25045k6xf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02344",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CC"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "stat.ML"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02344",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8tzn25045k6xf.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:21Z",
      "native_id": "2611.02344",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02344"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Efficient Proper Agnostic Learning of Halfspaces",
  "title_text": "Efficient Proper Agnostic Learning of Halfspaces",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:35Z",
  "url": "https://research.draconitic.com/paper/8tzn25045k6xf",
  "venue": "arXiv",
  "versions": []
}