  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.
