Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds

TL;DR

This paper introduces a new formulation of concentrated differential privacy using Renyi divergence, providing sharper analysis tools, establishing lower bounds, and unifying it with approximate differential privacy.

Contribution

It offers an alternative Renyi divergence-based formulation of concentrated differential privacy, leading to improved results and a unified framework with approximate differential privacy.

Findings

Sharper quantitative results for concentrated differential privacy

Lower bounds established for privacy guarantees

Unified framework with approximate differential privacy

Abstract

"Concentrated differential privacy" was recently introduced by Dwork and Rothblum as a relaxation of differential privacy, which permits sharper analyses of many privacy-preserving computations. We present an alternative formulation of the concept of concentrated differential privacy in terms of the Renyi divergence between the distributions obtained by running an algorithm on neighboring inputs. With this reformulation in hand, we prove sharper quantitative results, establish lower bounds, and raise a few new questions. We also unify this approach with approximate differential privacy by giving an appropriate definition of "approximate concentrated differential privacy."