{
  "abstract": "Gaussian differential privacy (GDP) and zero-concentrated differential privacy (zCDP) are two competing privacy accounting frameworks, but they share similar minimax lower bounds in various estimation problems. Moreover, it is known that a mechanism satisfying $μ$-GDP satisfies $(μ^2/2)$-zCDP, whereas the converse fails to hold at the same calibration. In this paper, we establish the optimal reverse conversion, showing that every $ρ$-zCDP mechanism satisfies $μ_{\\mathrm{zCDP}}(ρ)$-GDP, where $μ_{\\mathrm{zCDP}}(ρ)=2Φ^{-1}((1+e^{-t_ρ})^{-1})$ and $t_ρ$ uniquely solves the equation $ρ=t_ρ\\tanh(t_ρ/2)$. We also obtain simplified bounds $\\sqrt{πρ}\\leqμ_{\\mathrm{zCDP}}(ρ)\\leq\\sqrt{8ρ}$, with sharp constants, which imply equivalence of the two frameworks up to constants. This explains why their minimax risks agree up to a constant rescaling of the privacy budget. We show that the squared conversion is strictly convex, which implies that converting zCDP to GDP before applying composition or group privacy yields a tighter GDP guarantee than converting afterward. We also derive the sharp conversion from bounded-range and logistic DP mechanisms (e.g., exponential mechanism) to GDP, where converting before composition but after group privacy gives the tighter guarantee.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01218",
  "author_total": 3,
  "authors": [
    {
      "name": "Yu-Wei Chen"
    },
    {
      "name": "Aaradhya Pandey"
    },
    {
      "name": "Jordan Awan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/29p2x3swstzjf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01218",
  "fulltext_url": null,
  "id": "29p2x3swstzjf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01218",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01218",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/29p2x3swstzjf.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01218",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01218"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Optimal Conversion from Zero-Concentrated to Gaussian Differential Privacy",
  "title_text": "Optimal Conversion from Zero-Concentrated to Gaussian Differential Privacy",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:35Z",
  "url": "https://research.draconitic.com/paper/29p2x3swstzjf",
  "venue": "arXiv",
  "versions": []
}