Towards Fast and Energy-Efficient Hierarchical Federated Edge Learning: A Joint Design for Helper Scheduling and Resource Allocation

Hierarchical federated edge learning (H-FEEL) has been recently proposed to enhance the federated learning model. Such a system generally consists of three entities, i.e., the server, helpers, and clients. Each helper collects the trained gradients from users nearby, aggregates them, and sends the result to the server for model update. Due to limited communication resources, only a portion of helpers can upload their aggregated gradients to the server, thereby necessitating a well design for helper scheduling and communication resources allocation. In this paper, we develop a training algorithm for H-FEEL which involves local gradient computing, weighted gradient uploading, and model updating phases. By characterizing these phases mathematically and analyzing the one-round convergence bound of the training algorithm, we formulate a problem to achieve the scheduling and resource allocation scheme. 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 problem and helper scheduling problem. For the first subproblem, we obtain a low-complexity suboptimal solution by using a four-stage method. For the second subproblem, we obtain a stationary point by using the penalty convex-concave procedure. The efficacy of our scheme is demonstrated via simulations, and the analytical framework is shown to provide valuable insights for the design of practical H-FEEL system.