  This work investigates fault-resilient federated learning when the data
samples are non-uniformly distributed across workers, and the number of faulty
workers is unknown to the central server. In the presence of adversarially
faulty workers who may strategically corrupt datasets, the local messages
exchanged (e.g., local gradients and/or local model parameters) can be
unreliable, and thus the vanilla stochastic gradient descent (SGD) algorithm is
not guaranteed to converge. Recently developed algorithms improve upon vanilla
SGD by providing robustness to faulty workers at the price of slowing down
convergence. To remedy this limitation, the present work introduces a
fault-resilient proximal gradient (FRPG) algorithm that relies on Nesterov's
acceleration technique. To reduce the communication overhead of FRPG, a local
(L) FRPG algorithm is also developed to allow for intermittent server-workers
parameter exchanges. For strongly convex loss functions, FRPG and LFRPG have
provably faster convergence rates than a benchmark robust stochastic
aggregation algorithm. Moreover, LFRPG converges faster than FRPG while using
the same communication rounds. Numerical tests performed on various real
datasets confirm the accelerated convergence of FRPG and LFRPG over the robust
stochastic aggregation benchmark and competing alternatives.
