Duff: A Dataset-Distance-Based Utility Function Family for the Exponential Mechanism

TL;DR

Duff introduces a dataset-distance-based utility function family for the exponential mechanism in differential privacy, providing higher fidelity and better tail decay than existing methods, especially for median computation.

Contribution

This paper presents Duff, a novel utility function family that improves differential privacy mechanisms by leveraging dataset distances, with provable advantages over smooth sensitivity-based methods.

Findings

Duff often yields higher fidelity to true statistics.

It offers a noise distribution with variance proportional to smooth sensitivity.

Empirical results show practical advantages for median computation.

Abstract

We propose and analyze a general-purpose dataset-distance-based utility function family, Duff, for differential privacy's exponential mechanism. Given a particular dataset and a statistic (e.g., median, mode), this function family assigns utility to a possible output o based on the number of individuals whose data would have to be added to or removed from the dataset in order for the statistic to take on value o. We show that the exponential mechanism based on Duff often offers provably higher fidelity to the statistic's true value compared to existing differential privacy mechanisms based on smooth sensitivity. In particular, Duff is an affirmative answer to the open question of whether it is possible to have a noise distribution whose variance is proportional to smooth sensitivity and whose tails decay at a faster-than-polynomial rate. We conclude our paper with an empirical evaluation of the practical advantages of Duff for the task of computing medians.