Multi-Objective Optimization for Bandwidth-Limited Federated Learning in Wireless Edge Systems

This paper studies a bandwidth-limited federated learning (FL) system where the access point is a central server for aggregation and the energy-constrained user equipments (UEs) with limited computation capabilities (e.g., Internet of Things devices) perform local training. Limited by the bandwidth in wireless edge systems, only a part of UEs can participate in each FL training round. Selecting different UEs could affect the FL performance, and selected UEs need to allocate their computing resource effectively. In wireless edge FL systems, simultaneously accelerating FL training and reducing computing-communication energy consumption are of importance. To this end, we formulate a multi-objective optimization problem (MOP). In MOP, the model training convergence is difficult to calculate accurately. Meanwhile, MOP is a combinatorial optimization problem, with the high-dimension mix-integer variables, which is proved to be NP-hard. To address these challenges, a multi-objective evolutionary algorithm for the bandwidth-limited FL system (MOEA-FL) is proposed to obtain a Pareto optimal solution set. In MOEA-FL, an age-of-update-loss method is first proposed to transform the original global loss function into a convergence reference function. Then, MOEA-FL divides MOP into $N$ single objective subproblems by the Tchebycheff approach and optimizes the subproblems simultaneously by evolving a population. Extensive experiments have been carried out on MNIST dataset and a medical case called TissueMNIST dataset for both the i.i.d and non-i.i.d data setting. Experimental results demonstrate that MOEA-FL performs better than other algorithms and verify the robustness and scalability of MOEA-FL.