  Federated Learning (FL) allows multiple participating clients to train
machine learning models collaboratively while keeping their datasets local and
only exchanging the gradient or model updates with a coordinating server.
Existing FL protocols are vulnerable to attacks that aim to compromise data
privacy and/or model robustness. Recently proposed defenses focused on ensuring
either privacy or robustness, but not both. In this paper, we focus on
simultaneously achieving differential privacy (DP) and Byzantine robustness for
cross-silo FL, based on the idea of learning from history. The robustness is
achieved via client momentum, which averages the updates of each client over
time, thus reducing the variance of the honest clients and exposing the small
malicious perturbations of Byzantine clients that are undetectable in a single
round but accumulate over time. In our initial solution DP-BREM, DP is achieved
by adding noise to the aggregated momentum, and we account for the privacy cost
from the momentum, which is different from the conventional DP-SGD that
accounts for the privacy cost from the gradient. Since DP-BREM assumes a
trusted server (who can obtain clients' local models or updates), we further
develop the final solution called DP-BREM+, which achieves the same DP and
robustness properties as DP-BREM without a trusted server by utilizing secure
aggregation techniques, where DP noise is securely and jointly generated by the
clients. Both theoretical analysis and experimental results demonstrate that
our proposed protocols achieve better privacy-utility tradeoff and stronger
Byzantine robustness than several baseline methods, under different DP budgets
and attack settings.
