Optimization-Based GenQSGD for Federated Edge Learning

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.