Concurrent Composition of Interactive Mechanisms with Adaptive Privacy-loss Parameters

Abstract

Over recent decades, the predominance of data analysis algorithms has made privacy an increasingly greater concern. Differential privacy is one framework for providing privacy guarantees for analysis of sensitive data. A persistent research direction in differential privacy is providing theoretical support for all the variety of ways a data analyst can interact with a dataset, so that practical implementations can have provable privacy guarantees. This thesis is concerned with the setting in which an analyst interacting with a set of differentially-private mechanisms is interested in both adaptively interleaving queries between mechanisms and also creating new ones. Previous work has provided provable guarantees for the sequential composition of non-interactive mechanisms with adaptive privacy-loss parameters, and the concurrent composition of interactive mechanisms with pre-fixed privacy-loss parameters, but no work has addressed the setting in which both the interaction and the privacy-loss parameters can both be chosen adaptively. Hence, we study the concurrent composition of interactive differentially-private mechanisms with adaptively chosen privacy-loss parameters. We provide formulations of privacy filters and odometers, specialized interactive mechanisms that allow for concurrent composition and adaptive composition, and also provide support for privacy-loss tracking. We prove that every valid privacy filter and odometer for non-interactive mechanisms extends to the concurrent composition of interactive mechanisms if privacy loss is measured using $(\epsilon, \delta)$-DP, $f$-DP, or R'enyi DP of fixed order. Our results offer strong theoretical foundations for enabling full adaptivity in composing differentially private interactive mechanisms, showing that concurrency does not affect the privacy guarantees. This thesis allows simplifications for existing code repositories, and also widens the range of scenarios in which differentially-private mechanisms can be applied with robust privacy guarantees.