Optimal Maximal Leakage-Distortion Tradeoff

TL;DR

This paper investigates the privacy-utility tradeoff using maximal leakage and Hamming distortion, deriving optimal mechanisms for known and uncertain priors, and analyzing the impact of prior distribution and privacy budget distribution.

Contribution

It introduces a comprehensive analysis of maximal leakage-based privacy mechanisms under various prior knowledge scenarios and proposes optimal strategies for minimizing distortion.

Findings

Optimal mechanisms fully disclose high-probability symbols.

Suppression of low-probability symbols improves privacy.

More uniform priors lead to higher worst-case distortion.

Abstract

Most methods for publishing data with privacy guarantees introduce randomness into datasets which reduces the utility of the published data. In this paper, we study the privacy-utility tradeoff by taking maximal leakage as the privacy measure and the expected Hamming distortion as the utility measure. We study three different but related problems. First, we assume that the data-generating distribution (i.e., the prior) is known, and we find the optimal privacy mechanism that achieves the smallest distortion subject to a constraint on maximal leakage. Then, we assume that the prior belongs to some set of distributions, and we formulate a min-max problem for finding the smallest distortion achievable for the worst-case prior in the set, subject to a maximal leakage constraint. Lastly, we define a partial order on privacy mechanisms based on the largest distortion they generate. Our results show that when the prior distribution is known, the optimal privacy mechanism fully discloses symbols with the largest prior probabilities, and suppresses symbols with the smallest prior probabilities. Furthermore, we show that sets of priors that contain more uniform distributions lead to larger distortion, while privacy mechanisms that distribute the privacy budget more uniformly over the symbols create smaller worst-case distortion.