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Differential Privacy Under Multiple Selections

Authors Ashish Goel, Zhihao Jiang, Aleksandra Korolova, Kamesh Munagala, Sahasrajit Sarmasarkar

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  • \ccsdesc{Security and privacy~Privacy-preserving protocols}
Keywords
  • Differential Privacy
  • Mechanism Design and Multi-Selection

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Abstract

We consider the setting where a user with sensitive features wishes to obtain a recommendation from a server in a differentially private fashion. We propose a "multi-selection" architecture where the server can send back multiple recommendations and the user chooses one from these that matches best with their private features. When the user feature is one-dimensional - on an infinite line - and the accuracy measure is defined w.r.t some increasing function 𝔥(.) of the distance on the line, we precisely characterize the optimal mechanism that satisfies differential privacy. The specification of the optimal mechanism includes both the distribution of the noise that the user adds to its private value, and the algorithm used by the server to determine the set of results to send back as a response. We show that Laplace is an optimal noise distribution in this setting. Furthermore, we show that this optimal mechanism results in an error that is inversely proportional to the number of results returned when the function 𝔥(.) is the identity function.

Cite As Get BibTex

Ashish Goel, Zhihao Jiang, Aleksandra Korolova, Kamesh Munagala, and Sahasrajit Sarmasarkar. Differential Privacy Under Multiple Selections. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 8:1-8:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.FORC.2025.8

Author Details

Ashish Goel
  • Stanford University, CA, USA
Zhihao Jiang
  • Stanford University, CA, USA
Aleksandra Korolova
  • Princeton University, NJ, USA
Kamesh Munagala
  • Duke University, Durham, NC, USA
Sahasrajit Sarmasarkar
  • Stanford University, CA, USA

Funding

  • Korolova, Aleksandra: Supported by NSF award CNS-2344925.
  • Munagala, Kamesh: Supported by NSF awards CCF-2113798 and IIS-2402823.

Acknowledgements

SS is grateful to Sanath Kumar Krishnamurthy for the helpful discussion on the weak-duality proof and to Mohak Goyal for an insightful conversation on the generalized privacy definition in Appendix A.1.

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