  We introduce CYBER-0, the first zero-order optimization algorithm for
memory-and-communication efficient Federated Learning, resilient to Byzantine
faults. We show through extensive numerical experiments on the MNIST dataset
and finetuning RoBERTa-Large that CYBER-0 outperforms state-of-the-art
algorithms in terms of communication and memory efficiency while reaching
similar accuracy. We provide theoretical guarantees on its convergence for
convex loss functions.
