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Smooth Sensitivity Revisited: Towards Optimality

Authors Richard Hladík , Jakub Tětek

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  • Security and privacy → Privacy-preserving protocols
Keywords
  • differential privacy
  • smooth sensitivity

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Abstract

Smooth sensitivity is one of the most commonly used techniques for designing practical differentially private mechanisms. In this approach, one computes the smooth sensitivity of a given query q on the given input D and releases q(D) with noise added proportional to this smooth sensitivity. One question remains: what distribution should we pick the noise from? 
In this paper, we give a new class of distributions suitable for the use with smooth sensitivity, which we name the PolyPlace distribution. This distribution improves upon the state-of-the-art Student’s T distribution in terms of standard deviation by arbitrarily large factors, depending on a "smoothness parameter" γ, which one has to set in the smooth sensitivity framework. Moreover, our distribution is defined for a wider range of parameter γ, which can lead to significantly better performance. 
Furthermore, we prove that the PolyPlace distribution converges for γ → 0 to the Laplace distribution and so does its variance. This means that the Laplace mechanism is a limit special case of the PolyPlace mechanism. This implies that our mechanism is in a certain sense optimal for γ → 0.

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Richard Hladík and Jakub Tětek. Smooth Sensitivity Revisited: Towards Optimality. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 2:1-2:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.FORC.2025.2

Author Details

Richard Hladík
  • ETH Zurich, Switzerland
Jakub Tětek
  • INSAIT, Sofia University "St. Kliment Ohridski", Bulgaria

Funding

Partially funded by the Ministry of Education and Science of Bulgaria’s support for INSAIT as part of the Bulgarian National Roadmap for Research Infrastructure. Partially supported by the VILLUM Foundation grants 54451 and 16582.
  • Hladík, Richard: Supported in part by the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme (grant agreement No. 949272)

Acknowledgements

We would like to thank Rasmus Pagh and Adam Sealfon for helpful discussions. We would like to thank Rasmus Pagh for hosting Richard at the University of Copenhagen. Jakub worked on this paper while affiliated with BARC, University of Copenhagen. Richard partially worked on this paper while visiting BARC, University of Copenhagen.

References

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