  Federated learning (FL) has recently become a hot research topic, in which
Byzantine robustness, communication efficiency and privacy preservation are
three important aspects. However, the tension among these three aspects makes
it hard to simultaneously take all of them into account. In view of this
challenge, we theoretically analyze the conditions that a communication
compression method should satisfy to be compatible with existing
Byzantine-robust methods and privacy-preserving methods. Motivated by the
analysis results, we propose a novel communication compression method called
consensus sparsification (ConSpar). To the best of our knowledge, ConSpar is
the first communication compression method that is designed to be compatible
with both Byzantine-robust methods and privacy-preserving methods. Based on
ConSpar, we further propose a novel FL framework called FedREP, which is
Byzantine-robust, communication-efficient and privacy-preserving. We
theoretically prove the Byzantine robustness and the convergence of FedREP.
Empirical results show that FedREP can significantly outperform
communication-efficient privacy-preserving baselines. Furthermore, compared
with Byzantine-robust communication-efficient baselines, FedREP can achieve
comparable accuracy with the extra advantage of privacy preservation.
