Free Gap Estimates from the Exponential Mechanism, Sparse Vector, Noisy Max and Related Algorithms

TL;DR

This paper demonstrates that key private selection algorithms can release gap information between selected and non-selected items without extra privacy cost, enhancing accuracy and enabling more efficient algorithms.

Contribution

It reveals that exponential mechanism, noisy max, and sparse vector algorithms can release gap information for free, and introduces hybrid algorithms that optimize privacy budget usage.

Findings

Gap information can be released at no additional privacy cost.

Follow-up counting queries accuracy improves by up to 66%.

Proposes hybrid algorithms for dynamic privacy budget savings.

Abstract

Private selection algorithms, such as the Exponential Mechanism, Noisy Max and Sparse Vector, are used to select items (such as queries with large answers) from a set of candidates, while controlling privacy leakage in the underlying data. Such algorithms serve as building blocks for more complex differentially private algorithms. In this paper we show that these algorithms can release additional information related to the gaps between the selected items and the other candidates for free (i.e., at no additional privacy cost). This free gap information can improve the accuracy of certain follow-up counting queries by up to 66%. We obtain these results from a careful privacy analysis of these algorithms. Based on this analysis, we further propose novel hybrid algorithms that can dynamically save additional privacy budget.