Worst-Case Utility Privacy Mechanism via Pointwise Maximal Leakage

TL;DR

This paper introduces a new privacy mechanism based on Pointwise Maximal Leakage (PML) that optimizes worst-case utility while satisfying privacy constraints, offering advantages over Differential Privacy.

Contribution

It develops a computationally efficient, utility-safe privacy mechanism using PML that outperforms traditional methods in worst-case utility scenarios.

Findings

The proposed mechanism is optimal for worst-case utility with output support constraints.

PML-based mechanisms can set some conditional probabilities to zero, enhancing utility.

Numerical experiments demonstrate the effectiveness of the proposed approach.

Abstract

We propose a discrete privacy mechanism exploiting beneficial properties of the novel privacy measure Pointwise Maximal Leakage (PML). Given the utility assignment characterized by every input-output letter pair, we study the mechanism design problem that satisfies PML privacy guarantees and maximizes the worst-case utility. Unlike popular privacy measures like Differential Privacy (DP), PML allows us to set some conditional probabilities in the mechanism to be zero and thereby preventing the occurrence of some low utilities while preserving a strict PML constraint. We show that the utility-safe mechanism, with low computational complexity, is optimal for the worst-case utility problem with an additional constraint on the output support set. We finally demonstrate the effectiveness in several numerical experiments. Due to DP's inability to have zeros in the mechanism, the design of privacy mechanisms that optimize the worst-case utility is underexplored, and this work shows that PML is a privacy measure that is perfectly suited for this purpose.