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Nearly-Optimal Private Selection via Gaussian Mechanism

Authors Ethan Leeman , Pasin Manurangsi

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Subject Classification

ACM Subject Classification
  • Security and privacy
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Differentially Private Selection
  • Gaussian Mechanism

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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|).

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.FORC.2026.4

Author Details

Ethan Leeman
  • Google Research, New York, NY, USA
Pasin Manurangsi
  • Google Research, Bangkok, Thailand

Acknowledgements

We thank Charlie Harrison for introducing us to this problem and for subsequent insightful discussions. We also thank Thomas Steinke for helpful discussions.

References

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  2. Amos Beimel, Kobbi Nissim, and Uri Stemmer. Private learning and sanitization: Pure vs. approximate differential privacy. Theory Comput., 12(1):1-61, 2016. URL: https://doi.org/10.4086/TOC.2016.V012A001.
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  4. Cynthia Dwork, Krishnaram Kenthapadi, Frank McSherry, Ilya Mironov, and Moni Naor. Our data, ourselves: Privacy via distributed noise generation. In EUROCRYPT, pages 486-503, 2006. URL: https://doi.org/10.1007/11761679_29.
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  7. Anupam Gupta, Katrina Ligett, Frank McSherry, Aaron Roth, and Kunal Talwar. Differentially private combinatorial optimization. In SODA, pages 1106-1125, 2010. URL: https://doi.org/10.1137/1.9781611973075.90.
  8. Frank McSherry and Kunal Talwar. Mechanism design via differential privacy. In FOCS, pages 94-103, 2007. URL: https://doi.org/10.1109/FOCS.2007.41.
  9. Thomas Steinke. Open problem: Selection via low-sensitivity queries. DifferentialPrivacy.org, May 2025. URL: https://differentialprivacy.org/open-problem-selection/.
  10. Justin Whitehouse, Aaditya Ramdas, Ryan Rogers, and Steven Wu. Fully-adaptive composition in differential privacy. In ICML, pages 36990-37007, 2023. URL: https://proceedings.mlr.press/v202/whitehouse23a.html.
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