  Federated learning is a communication-efficient training process that
alternates between local training at the edge devices and averaging the updated
local model at the central server. Nevertheless, it is impractical to achieve a
perfect acquisition of the local models in wireless communication due to noise,
which also brings serious effects on federated learning. To tackle this
challenge, we propose a robust design for federated learning to alleviate the
effects of noise in this paper. Considering noise in the two aforementioned
steps, we first formulate the training problem as a parallel optimization for
each node under the expectation-based model and the worst-case model. Due to
the non-convexity of the problem, a regularization for the loss function
approximation method is proposed to make it tractable. Regarding the worst-case
model, we develop a feasible training scheme which utilizes the sampling-based
successive convex approximation algorithm to tackle the unavailable maxima or
minima noise condition and the non-convex issue of the objective function.
Furthermore, the convergence rates of both new designs are analyzed from a
theoretical point of view. Finally, the improvement of prediction accuracy and
the reduction of loss function are demonstrated via simulations for the
proposed designs.
