Federated learning (FL) enables collaborative model training among distributed devices without data sharing, but existing FL suffers from poor scalability because of global model synchronization. To address this issue, hierarchical federated learning (HFL) has been recently proposed to let edge servers aggregate models of devices in proximity, while synchronizing via the cloud periodically. However, a critical open challenge about how to make a good synchronization scheme (when devices and edges should be synchronized) is still unsolved. Devices are heterogeneous in computing and communication capability, and their data could be non-IID. No existing work can well synchronize various roles (\textit{e.g.}, devices and edges) in HFL to guarantee high learning efficiency and accuracy. In this paper, we propose a learning-based synchronization scheme for HFL systems. By collecting data such as edge models, CPU usage, communication time, \textit{etc}., we design a deep reinforcement learning-based approach to decide the frequencies of cloud aggregation and edge aggregation, respectively. The proposed scheme well considers device heterogeneity, non-IID data and device mobility, to maximize the training model accuracy while minimizing the energy overhead. Meanwhile, the convergence bound of the proposed synchronization scheme has been analyzed. And we build an HFL testbed and conduct the experiments with real data obtained from Raspberry Pi and Alibaba Cloud. Extensive experiments under various settings are conducted to confirm the effectiveness of \textit{Arena}.
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