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DOI: 10.4230/LIPIcs.FORC.2026.4

Nearly-Optimal Private Selection via Gaussian Mechanism

Authors: Ethan Leeman and Pasin Manurangsi

Published in: LIPIcs, Volume 368, 7th Symposium on Foundations of Responsible Computing (FORC 2026)

Abstract

Steinke [2025] recently asked the following intriguing open question: Can we solve the differentially private selection problem with nearly-optimal error by only (adaptively) invoking Gaussian mechanism on low-sensitivity queries? We resolve this question positively. In particular, for a candidate set 𝒴, we achieve error guarantee of Õ(log |𝒴|), which is within a factor of (log log |𝒴|)^{O(1)} of the exponential mechanism [McSherry and Talwar, 2007]. This improves on Steinke’s mechanism which achieves an error of O(log^{3/2} |𝒴|).

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Ethan Leeman and Pasin Manurangsi. Nearly-Optimal Private Selection via Gaussian Mechanism. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 4:1-4:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{leeman_et_al:LIPIcs.FORC.2026.4,
  author =	{Leeman, Ethan and Manurangsi, Pasin},
  title =	{{Nearly-Optimal Private Selection via Gaussian Mechanism}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{4:1--4:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-419-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{368},
  editor =	{Lin, Huijia (Rachel)},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2026.4},
  URN =		{urn:nbn:de:0030-drops-259750},
  doi =		{10.4230/LIPIcs.FORC.2026.4},
  annote =	{Keywords: Differentially Private Selection, Gaussian Mechanism}
}

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Nearly-Optimal Private Selection via Gaussian Mechanism

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