An Optimization Framework for Federated Edge Learning

This paper intends to optimize the overall implementing process of federated learning (FL) in practical edge computing systems. First, we present a general FL algorithm, namely GenQSGD+, whose parameters include the numbers of global and local iterations, mini-batch size, and step size sequence. Then, we analyze the convergence of GenQSGD+ with arbitrary algorithm parameters. Next, we optimize all the algorithm parameters of GenQSGD+ to minimize the energy cost under the constraints on the time cost, convergence error, and step size sequence. The resulting optimization problem is challenging due to its non-convexity and the presence of a dimension-varying vector variable and non-differentiable constraint functions. We transform the complicated problem into a more tractable nonconvex problem using the structural properties of the original problem and propose an iterative algorithm using general inner approximation (GIA) and complementary geometric programming (CGP) to obtain a KKT point. Finally, we numerically demonstrate remarkable gains of optimization-based GenQSGD+ over typical FL algorithms and the advancement of the proposed optimization framework for federated edge learning.