  Optimal algorithm design for federated learning (FL) remains an open problem.
This paper explores the full potential of FL in practical edge computing
systems where workers may have different computation and communication
capabilities, and quantized intermediate model updates are sent between the
server and workers. First, we present a general quantized parallel mini-batch
stochastic gradient descent (SGD) algorithm for FL, namely GenQSGD, which is
parameterized by the number of global iterations, the numbers of local
iterations at all workers, and the mini-batch size. We also analyze its
convergence error for any choice of the algorithm parameters. Then, we optimize
the algorithm parameters to minimize the energy cost under the time constraint
and convergence error constraint. The optimization problem is a challenging
non-convex problem with non-differentiable constraint functions. We propose an
iterative algorithm to obtain a KKT point using advanced optimization
techniques. Numerical results demonstrate the significant gains of GenQSGD over
existing FL algorithms and reveal the importance of optimally designing FL
algorithms.
