Privacy-Utility Tradeoff Based on $α$-lift

TL;DR

This work addresses designing privacy mechanisms under $α$-lift privacy with mutual information as the utility in a PUT setting. It proves that $α$-lift is convex in the lift and extends the known max-lift solution to the full range $α\in(1,∞]$ by developing a heuristic that leverages extreme points at $α=∞$. The proposed algorithm constructs feasible candidate solutions by combining $α=∞$ extremal points with convexity properties and solves a linear program to estimate the optimal utility $I(X;Y)$ for each $(α,ε)$. Numerical results demonstrate substantial PUT gains over baseline methods and delineate how the privacy budget $ε$ and the tunable parameter $α$ shape the tradeoff, providing practical guidance for privacy-utility design.

Abstract

Information density and its exponential form, known as lift, play a central role in information privacy leakage measures. $α$-lift is the power-mean of lift, which is tunable between the worst-case measure max-lift ($α=\infty$) and more relaxed versions ($α<\infty$). This paper investigates the optimization problem of the privacy-utility tradeoff (PUT) where $α$-lift and mutual information are privacy and utility measures, respectively. Due to the nonlinear nature of $α$-lift for $α<\infty$, finding the optimal solution is challenging. Therefore, we propose a heuristic algorithm to estimate the optimal utility for each value of $α$, inspired by the optimal solution for $α=\infty$ and the convexity of $α$-lift with respect to the lift, which we prove. The numerical results show the efficacy of the algorithm and indicate the effective range of $α$ and privacy budget $\varepsilon$ with good PUT performance.

Figures (1)

• Figure 1: Privacy-utility tradeoff for $\alpha$-lift as privacy measure and normalized mutual information as utility measure.

Theorems & Definitions (6)

• Definition 1
• Remark 1
• Remark 2
• Proposition 1
• Definition 2
• Proposition 2