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.
@InProceedings{hladik_et_al:LIPIcs.FORC.2025.2, author = {Hlad{\'\i}k, Richard and T\v{e}tek, Jakub}, title = {{Smooth Sensitivity Revisited: Towards Optimality}}, booktitle = {6th Symposium on Foundations of Responsible Computing (FORC 2025)}, pages = {2:1--2:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-367-6}, ISSN = {1868-8969}, year = {2025}, volume = {329}, editor = {Bun, Mark}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.2}, URN = {urn:nbn:de:0030-drops-231292}, doi = {10.4230/LIPIcs.FORC.2025.2}, annote = {Keywords: differential privacy, smooth sensitivity} }
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