  In the federated learning setting, multiple clients jointly train a model
under the coordination of the central server, while the training data is kept
on the client to ensure privacy. Normally, inconsistent distribution of data
across different devices in a federated network and limited communication
bandwidth between end devices impose both statistical heterogeneity and
expensive communication as major challenges for federated learning. This paper
proposes an algorithm to achieve more fairness and accuracy in federated
learning (FedFa). It introduces an optimization scheme that employs a double
momentum gradient, thereby accelerating the convergence rate of the model. An
appropriate weight selection algorithm that combines the information quantity
of training accuracy and training frequency to measure the weights is proposed.
This procedure assists in addressing the issue of unfairness in federated
learning due to preferences for certain clients. Our results show that the
proposed FedFa algorithm outperforms the baseline algorithm in terms of
accuracy and fairness.
