  Federated learning (FL) is an emerging paradigm that allows a central server
to train machine learning models using remote users' data. Despite its growing
popularity, FL faces challenges in preserving the privacy of local datasets,
its sensitivity to poisoning attacks by malicious users, and its communication
overhead. The latter is additionally considerably dominant in large-scale
networks. These limitations are often individually mitigated by local
differential privacy (LDP) mechanisms, robust aggregation, compression, and
user selection techniques, which typically come at the cost of accuracy. In
this work, we present compressed private aggregation (CPA), that allows massive
deployments to simultaneously communicate at extremely low bit rates while
achieving privacy, anonymity, and resilience to malicious users. CPA randomizes
a codebook for compressing the data into a few bits using nested lattice
quantizers, while ensuring anonymity and robustness, with a subsequent
perturbation to hold LDP. The proposed CPA is proven to result in FL
convergence in the same asymptotic rate as FL without privacy, compression, and
robustness considerations, while satisfying both anonymity and LDP
requirements. These analytical properties are empirically confirmed in a
numerical study, where we demonstrate the performance gains of CPA compared
with separate mechanisms for compression and privacy for training different
image classification models, as well as its robustness in mitigating the
harmful effects of malicious users.
