An Optimization Framework for Federated Edge Learning

The optimal design of federated learning (FL) algorithms for solving general machine learning (ML) problems in practical edge computing systems with quantized message passing remains an open problem. This paper considers an edge computing system where the server and workers have possibly different computing and communication capabilities and employ quantization before transmitting messages. To explore the full potential of FL in such an edge computing system, we first present a general FL algorithm, namely GenQSGD, parameterized by the numbers of global and local iterations, mini-batch size, and step size sequence. Then, we analyze its convergence for an arbitrary step size sequence and specify the convergence results under three commonly adopted step size rules, namely the constant, exponential, and diminishing step size rules. Next, we optimize the algorithm parameters to minimize the energy cost under the time constraint and convergence error constraint, with the focus on the overall implementing process of FL. Specifically, for any given step size sequence under each considered step size rule, we optimize the numbers of global and local iterations and mini-batch size to optimally implement FL for applications with preset step size sequences. We also optimize the step size sequence along with these algorithm parameters to explore the full potential of FL. The resulting optimization problems are challenging non-convex problems with non-differentiable constraint functions. We propose iterative algorithms to obtain KKT points using general inner approximation (GIA) and tricks for solving complementary geometric programming (CGP). Finally, we numerically demonstrate the remarkable gains of GenQSGD with optimized algorithm parameters over existing FL algorithms and reveal the significance of optimally designing general FL algorithms.