FedHelo: Hierarchical Federated Learning With Loss-Based-Heterogeneity in Wireless Networks

Hierarchical federated learning (HFL) in wireless networks significantly saves communication resources due to edge aggregation conducted in edge mobile computing (MEC) servers. Taking into account the spatially correlated characteristics of data in wireless networks, in this paper, we analyze the performance of HFL with hybrid data distributions, i.e. intra-MEC independent and identically distributed (IID) and inter-MEC non-IID data samples. We derive the upper bound of the difference between the achieved loss and the minimum one, which reveals the impacts of data heterogeneity and global aggregation frequency on the performance of HFL. On this basis, we propose an algorithm named FedHelo which optimizes the aggregation weights and edge/global aggregation frequencies under the constraints of training delay and clients' energy consumption. Our experiments <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i)</i> verify the obtained theoretical results; <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ii)</i> demonstrate the performance improvement achieved by FedHelo with the optimal aggregation weights and training/aggregation frequencies, especially in the scenario with high data heterogeneity; and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">iii)</i> show the preference for edge aggregation in the scenario with a tight delay or client's energy constraint.