Joint Scheduling and Resource Allocation for Hierarchical Federated Edge Learning

The concept of hierarchical federated edge learning (H-FEEL) has been recently proposed as an enhancement of federated learning model. Such a system generally consists of three entities, i.e., the server, helpers, and clients, in which each helper collects the trained gradients from clients nearby, aggregates them, and sends the result to the server for global model update. Due to limited communication resources, only a portion of helpers can be scheduled to upload their aggregated gradients in each round of the model training. And that necessitates a well-designed scheme for the joint helper scheduling and communication resources allocation. In this paper, we develop a training algorithm for the H-FEEL system which involves local gradient computing, weighted gradient uploading, and machine learning model updating phases. By characterizing these phases mathematically and analyzing one-round convergence bound of the training algorithm, we formulate an optimization problem to achieve the scheduling and resource allocation scheme. The problem simultaneously captures the uncertainty of the wireless channel and the importance of the weighted gradient. To solve the problem, we first transform it into an equivalent problem and then decompose the transformed problem into two subproblems: bit and sub-channel allocation and helper scheduling, which are mixed integer nonlinear programming and continuous nonlinear problems, respectively. For the first subproblem, we obtain an optimal solution of exponential complexity and a suboptimal solution that has polynomial complexity. For the second subproblem, we obtain a closed-form optimal solution in a special case and a suboptimal solution in the general case. The efficacy of our scheme is amply demonstrated via simulations and the analytical framework is shown to provide valuable design insights for the practical implementation of the H-FEEL system.