  There is an increasing interest in a fast-growing machine learning technique
called Federated Learning, in which the model training is distributed over
mobile user equipments (UEs), exploiting UEs' local computation and training
data. Despite its advantages in data privacy-preserving, Federated Learning
(FL) still has challenges in heterogeneity across UEs' data and physical
resources. We first propose a FL algorithm which can handle the heterogeneous
UEs' data challenge without further assumptions except strongly convex and
smooth loss functions. We provide the convergence rate characterizing the
trade-off between local computation rounds of UE to update its local model and
global communication rounds to update the FL global model. We then employ the
proposed FL algorithm in wireless networks as a resource allocation
optimization problem that captures the trade-off between the FL convergence
wall clock time and energy consumption of UEs with heterogeneous computing and
power resources. Even though the wireless resource allocation problem of FL is
non-convex, we exploit this problem's structure to decompose it into three
sub-problems and analyze their closed-form solutions as well as insights to
problem design. Finally, we illustrate the theoretical analysis for the new
algorithm with Tensorflow experiments and extensive numerical results for the
wireless resource allocation sub-problems. The experiment results not only
verify the theoretical convergence but also show that our proposed algorithm
outperforms the vanilla FedAvg algorithm in terms of convergence rate and
testing accuracy.
