Group Privacy Amplification and Unified Amplification by Subsampling for
  Rényi Differential Privacy
Jan Schuchardt Mihail Stoian Arthur Kosmala Stephan Günnemann
Differential privacy (DP) has various desirable properties, such as
robustness to post-processing, group privacy, and amplification by subsampling,
which can be derived independently of each other. Our goal is to determine
whether stronger privacy guarantees can be obtained by considering multiple of
these properties jointly. To this end, we focus on the combination of group
privacy and amplification by subsampling. To provide guarantees that are
amenable to machine learning algorithms, we conduct our analysis in the
framework of R\'enyi-DP, which has more favorable composition properties than
$(\epsilon,\delta)$-DP. As part of this analysis, we develop a unified
framework for deriving amplification by subsampling guarantees for R\'enyi-DP,
which represents the first such framework for a privacy accounting method and
is of independent interest. We find that it not only lets us improve upon and
generalize existing amplification results for R\'enyi-DP, but also derive
provably tight group privacy amplification guarantees stronger than existing
principles. These results establish the joint study of different DP properties
as a promising research direction.