Robust Privacy-Utility Tradeoffs under Differential Privacy and Hamming Distortion

TL;DR

This paper develops a framework for balancing privacy and utility in data sharing using differential privacy, categorizing source distributions and deriving optimal mechanisms and bounds for various cases.

Contribution

It introduces a comprehensive privacy-utility tradeoff analysis for finite source sets, including optimal mechanisms and bounds based on source distribution properties.

Findings

Symmetric DP mechanisms are optimal for convex hulls including the uniform distribution.

Asymmetric DP mechanisms are optimal for source sets with fixed monotonic probability orderings.

General bounds and conditions for tightness are established for other source sets.

Abstract

A privacy-utility tradeoff is developed for an arbitrary set of finite-alphabet source distributions. Privacy is quantified using differential privacy (DP), and utility is quantified using expected Hamming distortion maximized over the set of distributions. The family of source distribution sets (source sets) is categorized into three classes, based on different levels of prior knowledge they capture. For source sets whose convex hull includes the uniform distribution, symmetric DP mechanisms are optimal. For source sets whose probability values have a fixed monotonic ordering, asymmetric DP mechanisms are optimal. For all other source sets, general upper and lower bounds on the optimal privacy leakage are developed and a necessary and sufficient condition for tightness are established. Differentially private leakage is an upper bound on mutual information (MI) leakage: the two criteria are compared analytically and numerically to illustrate the effect of adopting a stronger privacy criterion.