{
  "abstract": "We study differentially private black-box evaluation of arbitrary high-dimensional functions. Given a dataset $S$ and query access to a function $f$---whose sensitivity may be unknown or unbounded---the goal is to privately output an approximation to $f(S)$. The black-box evaluator can only query the value of $f$ over a down neighborhood of $S$ (i.e., those subsets of $S$ that are obtained by removing a bounded number of elements from $S$). We design generic black-box evaluators for both pure and approximate differential privacy through a reduction to high-dimensional private quasi-concave optimization (QCO). Our black-box evaluator enjoys a geometric notion of utility. Consider the vectors obtained by applying $f$ on sets in a down neighborhood of $S$. With high probability, the evaluator's output is guaranteed to be in the convex hull of these vectors. Our work generalizes the result of Linder et al. [LRSS25] for real-valued function evaluation to high dimensions. It also recovers the private center-point guarantees of Beimel et al. [BMNS19], with an explicit additive approximation to maximum Tukey depth. We also apply our evaluators to user-level quasi-concave and convex optimization, showing how they can improve upon the sample-and-aggregate baseline of Nissim et al. [NRS07] by replacing the multiplicative data overhead with an additive overhead. Finally, we show that our formulation of high dimensional black-box evaluation and high dimensional private QCO are equivalent up to a factor of the dimension: the hardest private evaluation instances already arise from the cases that $f$ is a (non-private) quasi-concave optimizer.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24477",
  "author_total": 3,
  "authors": [
    {
      "name": "Mohammad Afzali"
    },
    {
      "name": "Hassan Ashtiani"
    },
    {
      "name": "Adam Smith"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/00gntfb4k4g1f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24477",
  "fulltext_url": null,
  "id": "00gntfb4k4g1f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24477",
  "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.CR"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Privacy-Preserving Technologies in Data"
    ]
  ],
  "openalex": "W7223000710",
  "pdf_url": "https://arxiv.org/pdf/2610.24477",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/00gntfb4k4g1f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24477",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24477"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Private Evaluation of High-Dimensional Functions",
  "title_text": "Private Evaluation of High-Dimensional Functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:54Z",
  "url": "https://research.draconitic.com/paper/00gntfb4k4g1f",
  "venue": "arXiv",
  "versions": []
}