Exponential Randomized Response: Boosting Utility in Differentially Private Selection

TL;DR

This paper introduces a new differentially private selection mechanism that significantly improves utility over existing methods like the exponential mechanism and permute-and-flip, especially in common scenarios.

Contribution

A novel differentially private selection mechanism with theoretical and empirical advantages over existing methods, offering larger utility improvements in typical cases.

Findings

Utility improvements of up to a factor of several times over existing mechanisms.

The new mechanism performs better in common scenarios but may have lower utility in niche cases.

Empirical results confirm theoretical advantages.

Abstract

A differentially private selection algorithm outputs from a finite set the item that approximately maximizes a data-dependent quality function. The most widely adopted mechanisms tackling this task are the pioneering exponential mechanism and permute-and-flip, which can offer utility improvements of up to a factor of two over the exponential mechanism. This work introduces a new differentially private mechanism for private selection and conducts theoretical and empirical comparisons with the above mechanisms. For reasonably common scenarios, our mechanism can provide utility improvements of factors significantly larger than two over the exponential and permute-and-flip mechanisms. Because the utility can deteriorate in niche scenarios, we recommend our mechanism to analysts who can tolerate lower utility for some datasets.