  Federated learning (FL) is a useful tool in distributed machine learning that
utilizes users' local datasets in a privacy-preserving manner. When deploying
FL in a constrained wireless environment; however, training models in a
time-efficient manner can be a challenging task due to intermittent
connectivity of devices, heterogeneous connection quality, and non-i.i.d. data.
In this paper, we provide a novel convergence analysis of non-convex loss
functions using FL on both i.i.d. and non-i.i.d. datasets with arbitrary device
selection probabilities for each round. Then, using the derived convergence
bound, we use stochastic optimization to develop a new client selection and
power allocation algorithm that minimizes a function of the convergence bound
and the average communication time under a transmit power constraint. We find
an analytical solution to the minimization problem. One key feature of the
algorithm is that knowledge of the channel statistics is not required and only
the instantaneous channel state information needs to be known. Using the
FEMNIST and CIFAR-10 datasets, we show through simulations that the
communication time can be significantly decreased using our algorithm, compared
to uniformly random participation.
