Bounds for Privacy-Utility Trade-off with Non-zero Leakage

TL;DR

This paper derives bounds on the privacy-utility trade-off in two data sharing scenarios, allowing for non-zero leakage, and improves existing bounds when no leakage is permitted.

Contribution

It extends the Functional Representation Lemma to relax independence constraints, providing new bounds for privacy-utility trade-offs with controlled leakage.

Findings

Derived lower bounds for privacy-utility trade-off with leakage.

Established upper bounds for both scenarios.

Improved bounds for the case of zero leakage.

Abstract

The design of privacy mechanisms for two scenarios is studied where the private data is hidden or observable. In the first scenario, an agent observes useful data $Y$, which is correlated with private data $X$, and wants to disclose the useful information to a user. A privacy mechanism is employed to generate data $U$ that maximizes the revealed information about $Y$ while satisfying a privacy criterion. In the second scenario, the agent has additionally access to the private data. To this end, the Functional Representation Lemma and Strong Functional Representation Lemma are extended relaxing the independence condition and thereby allowing a certain leakage. Lower bounds on privacy-utility trade-off are derived for the second scenario as well as upper bounds for both scenarios. In particular, for the case where no leakage is allowed, our upper and lower bounds improve previous bounds.