Private Lossless Multiple Release

2025-05-28

AI Summary

This work addresses the problem of multiple releases under differential privacy in multi-level trust settings. We propose the first lossless multi-release mechanism: for arbitrarily ordered releases with heterogeneous privacy parameters (εᵢ), the composition privacy guarantee of any subset S is strictly equal to min{εᵢ ∣ i ∈ S}, and each release’s output distribution is identical to that of an independent single release. Methodologically, we develop a unified framework based on additive noise (Gaussian, Laplace, Poisson), eliminating reliance on Brownian motion and enabling concise, rigorous privacy analysis. For sparse histograms, we further optimize the mechanism so that its asymptotic time complexity is independent of data dimensionality. Our key contribution is the first realization of strictly lossless, parameter-heterogeneous, order-agnostic multiple private releases—breaking the sequential constraints inherent in conventional incremental mechanisms. This advances both theoretical guarantees (exact composition) and practical efficiency (dimension-free runtime, unified noise design).

Technology Category

• Machine Learning: Privacy
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

Koufogiannis et al. (2016) showed a $ extit{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 $ extit{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 $ extit{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.

Problem

• Generalizes multiple private data releases with varying privacy levels
• Ensures lossless privacy guarantees across combined releases
• Provides efficient methods for additive noise mechanisms

Innovation

• Lossless multiple release for additive noise mechanisms
• Simple Gaussian method without Brownian motion
• Efficient gradual release for sparse histograms