Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergences

TL;DR

This paper introduces a unified, rigorous framework for analyzing privacy amplification by subsampling in differential privacy, improving existing bounds and deriving new results using divergence characterizations and advanced mathematical tools.

Contribution

It presents a general method that recovers, improves, and extends prior analyses of privacy amplification, introducing new tools like privacy profiles and advanced joint convexity.

Findings

Provides tighter bounds for privacy amplification

Derives new instances of privacy amplification effects

Unifies analysis of different subsampling methods

Abstract

Differential privacy comes equipped with multiple analytical tools for the design of private data analyses. One important tool is the so-called "privacy amplification by subsampling" principle, which ensures that a differentially private mechanism run on a random subsample of a population provides higher privacy guarantees than when run on the entire population. Several instances of this principle have been studied for different random subsampling methods, each with an ad-hoc analysis. In this paper we present a general method that recovers and improves prior analyses, yields lower bounds and derives new instances of privacy amplification by subsampling. Our method leverages a characterization of differential privacy as a divergence which emerged in the program verification community. Furthermore, it introduces new tools, including advanced joint convexity and privacy profiles, which might be of independent interest.