  To enable large-scale machine learning in bandwidth-hungry environments such
as wireless networks, significant progress has been made recently in designing
communication-efficient federated learning algorithms with the aid of
communication compression. On the other end, privacy-preserving, especially at
the client level, is another important desideratum that has not been addressed
simultaneously in the presence of advanced communication compression techniques
yet. In this paper, we propose a unified framework that enhances the
communication efficiency of private federated learning with communication
compression. Exploiting both general compression operators and local
differential privacy, we first examine a simple algorithm that applies
compression directly to differentially-private stochastic gradient descent, and
identify its limitations. We then propose a unified framework SoteriaFL for
private federated learning, which accommodates a general family of local
gradient estimators including popular stochastic variance-reduced gradient
methods and the state-of-the-art shifted compression scheme. We provide a
comprehensive characterization of its performance trade-offs in terms of
privacy, utility, and communication complexity, where SoteraFL is shown to
achieve better communication complexity without sacrificing privacy nor utility
than other private federated learning algorithms without communication
compression.
