Private Lossless Multiple Release

Joel Daniel Andersson, Lukas Retschmeier, Boel Nelson, Rasmus Pagh
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:1534-1553, 2025.

Abstract

Koufogiannis et al. (2016) showed a $\textit{gradual release}$ result for Laplace noise-based differentially private mechanisms: given an $\varepsilon$-DP release, a new release with privacy parameter $\varepsilon’ > \varepsilon$ can be computed such that the combined privacy loss of both releases is at most $\varepsilon’$ and the distribution of the latter is the same as a single release with parameter $\varepsilon’$. They also showed gradual release techniques for Gaussian noise, later also explored by Whitehouse et al. (2022). In this paper, we consider a more general $\textit{multiple release}$ setting in which analysts hold private releases with different privacy parameters corresponding to different access/trust levels. These releases are determined one by one, with privacy parameters in arbitrary order. A multiple release is $\textit{lossless}$ if having access to a subset $S$ of the releases has the same privacy guarantee as the least private release in $S$, and each release has the same distribution as a single release with the same privacy parameter. Our main result is that lossless multiple release is possible for a large class of additive noise mechanisms. For the Gaussian mechanism we give a simple method for lossless multiple release with a short, self-contained analysis that does not require knowledge of the mathematics of Brownian motion. We also present lossless multiple release for the Laplace and Poisson mechanisms. Finally, we consider how to efficiently do gradual release of sparse histograms, and present a mechanism with running time independent of the number of dimensions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-andersson25a, title = {Private Lossless Multiple Release}, author = {Andersson, Joel Daniel and Retschmeier, Lukas and Nelson, Boel and Pagh, Rasmus}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {1534--1553}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/andersson25a/andersson25a.pdf}, url = {https://proceedings.mlr.press/v267/andersson25a.html}, abstract = {Koufogiannis et al. (2016) showed a $\textit{gradual release}$ result for Laplace noise-based differentially private mechanisms: given an $\varepsilon$-DP release, a new release with privacy parameter $\varepsilon’ > \varepsilon$ can be computed such that the combined privacy loss of both releases is at most $\varepsilon’$ and the distribution of the latter is the same as a single release with parameter $\varepsilon’$. They also showed gradual release techniques for Gaussian noise, later also explored by Whitehouse et al. (2022). In this paper, we consider a more general $\textit{multiple release}$ setting in which analysts hold private releases with different privacy parameters corresponding to different access/trust levels. These releases are determined one by one, with privacy parameters in arbitrary order. A multiple release is $\textit{lossless}$ if having access to a subset $S$ of the releases has the same privacy guarantee as the least private release in $S$, and each release has the same distribution as a single release with the same privacy parameter. Our main result is that lossless multiple release is possible for a large class of additive noise mechanisms. For the Gaussian mechanism we give a simple method for lossless multiple release with a short, self-contained analysis that does not require knowledge of the mathematics of Brownian motion. We also present lossless multiple release for the Laplace and Poisson mechanisms. Finally, we consider how to efficiently do gradual release of sparse histograms, and present a mechanism with running time independent of the number of dimensions.} }
Endnote
%0 Conference Paper %T Private Lossless Multiple Release %A Joel Daniel Andersson %A Lukas Retschmeier %A Boel Nelson %A Rasmus Pagh %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-andersson25a %I PMLR %P 1534--1553 %U https://proceedings.mlr.press/v267/andersson25a.html %V 267 %X Koufogiannis et al. (2016) showed a $\textit{gradual release}$ result for Laplace noise-based differentially private mechanisms: given an $\varepsilon$-DP release, a new release with privacy parameter $\varepsilon’ > \varepsilon$ can be computed such that the combined privacy loss of both releases is at most $\varepsilon’$ and the distribution of the latter is the same as a single release with parameter $\varepsilon’$. They also showed gradual release techniques for Gaussian noise, later also explored by Whitehouse et al. (2022). In this paper, we consider a more general $\textit{multiple release}$ setting in which analysts hold private releases with different privacy parameters corresponding to different access/trust levels. These releases are determined one by one, with privacy parameters in arbitrary order. A multiple release is $\textit{lossless}$ if having access to a subset $S$ of the releases has the same privacy guarantee as the least private release in $S$, and each release has the same distribution as a single release with the same privacy parameter. Our main result is that lossless multiple release is possible for a large class of additive noise mechanisms. For the Gaussian mechanism we give a simple method for lossless multiple release with a short, self-contained analysis that does not require knowledge of the mathematics of Brownian motion. We also present lossless multiple release for the Laplace and Poisson mechanisms. Finally, we consider how to efficiently do gradual release of sparse histograms, and present a mechanism with running time independent of the number of dimensions.
APA
Andersson, J.D., Retschmeier, L., Nelson, B. & Pagh, R.. (2025). Private Lossless Multiple Release. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:1534-1553 Available from https://proceedings.mlr.press/v267/andersson25a.html.

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