Privacy Under Hard Distortion Constraints

TL;DR

This paper investigates data disclosure with strict fidelity guarantees using hard distortion constraints and analyzes the privacy-utility tradeoff with maximal α-leakage, revealing invariance of optimal mechanisms across different leakage measures.

Contribution

It introduces a framework for privacy-utility tradeoff under hard distortion constraints using maximal α-leakage, showing invariance of solutions for all α>1.

Findings

Optimal mechanisms are invariant for all α>1.

Maximal leakage and mutual information are the extremal cases of the leakage measure.

Hard distortion constraints provide deterministic fidelity guarantees.

Abstract

We study the problem of data disclosure with privacy guarantees, wherein the utility of the disclosed data is ensured via a \emph{hard distortion} constraint. Unlike average distortion, hard distortion provides a deterministic guarantee of fidelity. For the privacy measure, we use a tunable information leakage measure, namely \textit{maximal $\alpha$-leakage} ($\alpha\in[1,\infty]$), and formulate the privacy-utility tradeoff problem. The resulting solution highlights that under a hard distortion constraint, the nature of the solution remains unchanged for both local and non-local privacy requirements. More precisely, we show that both the optimal mechanism and the optimal tradeoff are invariant for any $\alpha>1$; i.e., the tunable leakage measure only behaves as either of the two extrema, i.e., mutual information for $\alpha=1$ and maximal leakage for $\alpha=\infty$.