Composition in Differential Privacy for General Granularity Notions (Long Version)

TL;DR

This paper develops a comprehensive framework for differential privacy composition that applies to general neighborhood notions and data domains, improving accuracy in privacy loss estimation across various settings.

Contribution

It introduces a general composition theorem for differential privacy applicable to any neighborhood definition and data domain, covering multiple DP variants and settings.

Findings

Unified composition theorems for independent and adaptive cases

Enhanced accuracy in privacy loss estimation

Applicability to various DP variants and neighborhood notions

Abstract

The composition theorems of differential privacy (DP) allow data curators to combine different algorithms to obtain a new algorithm that continues to satisfy DP. However, new granularity notions (i.e., neighborhood definitions), data domains, and composition settings have appeared in the literature that the classical composition theorems do not cover. For instance, the original parallel composition theorem does not translate well to general granularity notions. This complicates the opportunity of composing DP mechanisms in new settings and obtaining accurate estimates of the incurred privacy loss after composition. To overcome these limitations, we study the composability of DP in a general framework and for any kind of data domain or neighborhood definition. We give a general composition theorem in both independent and adaptive versions and we provide analogous composition results for approximate, zero-concentrated, and Gaussian DP. Besides, we study the hypothesis needed to obtain the best composition bounds. Our theorems cover both parallel and sequential composition settings. Importantly, they also cover every setting in between, allowing us to compute the final privacy loss of a composition with greatly improved accuracy.