Privacy-Utility Trade-offs Under Multi-Level Point-Wise Leakage Constraints

2026-01-08

arXiv.org

AI Summary

This study addresses the challenge of maximizing utility in data disclosure under strict privacy constraints, where private data are inaccessible and each data point must satisfy a differential privacy leakage bound. The authors propose a multi-level pointwise leakage metric that transcends the conventional uniform threshold, enabling a hybrid regime combining full privacy and partial leakage. Leveraging information geometry, they derive a local quadratic approximation of mutual information under small leakage regimes, reformulating the problem as a constrained quadratic optimization solvable efficiently via singular value decomposition. Theoretically, they prove that when the leakage matrix is invertible, optimal utility can be achieved with merely binary outputs, for which a closed-form solution is provided—substantially simplifying mechanism design while preserving maximal information utility.

Technology Category

Machine Learning: PrivacyConstraint Satisfaction and Optimization: Constraint Learning and AcquisitionReasoning under Uncertainty: Stochastic Optimization

Application Category

Security and Privacy: Data transparency and provenanceUser Modeling, Personalization and Recommendation: User privacy protection in personalized systemsResponsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

An information-theoretic privacy mechanism design is studied, where an agent observes useful data $Y$ which is correlated with the private data $X$. The agent wants to reveal the information to a user, hence, the agent utilizes a privacy mechanism to produce disclosed data $U$ that can be revealed. We assume that the agent has no direct access to $X$, i.e., the private data is hidden. We study privacy mechanism design that maximizes the disclosed information about $Y$, measured by the mutual information between $Y$ and $U$, while satisfying a point-wise constraint with different privacy leakage budgets. We introduce a new measure, called the \emph{multi-level point-wise leakage}, which allows us to impose different leakage levels for different realizations of $U$. In contrast to previous studies on point-wise measures, which use the same leakage level for each realization, we consider a more general scenario in which each data point can leak information up to a different threshold. As a result, this concept also covers cases in which some data points should not leak any information about the private data, i.e., they must satisfy perfect privacy. In other words, a combination of perfect privacy and non-zero leakage can be considered. When the leakage is sufficiently small, concepts from information geometry allow us to locally approximate the mutual information. We show that when the leakage matrix $P_{X|Y}$ is invertible, utilizing this approximation leads to a quadratic optimization problem that has closed-form solution under some constraints. In particular, we show that it is sufficient to consider only binary $U$ to attain the optimal utility. This leads to simple privacy designs with low complexity which are based on finding the maximum singular value and singular vector of a matrix.

Problem

• privacy-utility trade-off
• multi-level point-wise leakage
• perfect privacy
• mutual information
• privacy mechanism design

Innovation

• multi-level point-wise leakage
• privacy-utility trade-off
• information geometry
• quadratic optimization
• singular value decomposition