  Federated learning (FL) enables clients to collaboratively train machine
learning models under the coordination of a server in a privacy-preserving
manner. One of the main challenges in FL is that the server may not receive
local updates from each client in each round due to client resource limitations
and intermittent network connectivity. The existence of unavailable clients
severely deteriorates the overall FL performance. In this paper, we propose , a
novel client update Approximation and Rectification algorithm for FL to address
the client unavailability issue. FedAR can get all clients involved in the
global model update to achieve a high-quality global model on the server, which
also furnishes accurate predictions for each client. To this end, the server
uses the latest update from each client as a surrogate for its current update.
It then assigns a different weight to each client's surrogate update to derive
the global model, in order to guarantee contributions from both available and
unavailable clients. Our theoretical analysis proves that FedAR achieves
optimal convergence rates on non-IID datasets for both convex and non-convex
smooth loss functions. Extensive empirical studies show that FedAR
comprehensively outperforms state-of-the-art FL baselines including FedAvg,
MIFA, FedVARP and Scaffold in terms of the training loss, test accuracy, and
bias mitigation. Moreover, FedAR also depicts impressive performance in the
presence of a large number of clients with severe client unavailability.
