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In this paper, we propose Hierarchical Federated Learning with Momentum Acceleration (HierMo), a three-tier worker-edge-cloud federated learning algorithm that applies momentum for training acceleration. Momentum is calculated and aggregated in the three tiers. We provide convergence analysis for HierMo, showing a convergence rate of O(1/T). In the analysis, we develop a new approach to characterize model aggregation, momentum aggregation, and their interactions. Based on this result, {we prove that HierMo achieves a tighter convergence upper bound compared with HierFAVG without momentum}. We also propose HierOPT, which optimizes the aggregation periods (worker-edge and edge-cloud aggregation periods) to minimize the loss given a limited training time., Comment: 18 pages, 5 figures

Federated learning (FL) is a fast-developing technique that allows multiple workers to train a global model based on a distributed dataset. Conventional FL (FedAvg) employs gradient descent algorithm, which may not be efficient enough. Momentum is able to improve the situation by adding an additional momentum step to accelerate the convergence and has demonstrated its benefits in both centralized and FL environments. It is well-known that Nesterov Accelerated Gradient (NAG) is a more advantageous form of momentum, but it is not clear how to quantify the benefits of NAG in FL so far. This motives us to propose FedNAG, which employs NAG in each worker as well as NAG momentum and model aggregation in the aggregator. We provide a detailed convergence analysis of FedNAG and compare it with FedAvg. Extensive experiments based on real-world datasets and trace-driven simulation are conducted, demonstrating that FedNAG increases the learning accuracy by 3-24% and decreases the total training time by 11-70% compared with the benchmarks under a wide range of settings., Comment: publised in TPDS. 18 pages, 6 figures