  Federated learning is a collaborative machine learning framework to train
deep neural networks without accessing clients' private data. Previous works
assume one central parameter server either at the cloud or at the edge. A cloud
server can aggregate knowledge from all participating clients but suffers high
communication overhead and latency, while an edge server enjoys more efficient
communications during model update but can only reach a limited number of
clients. This paper exploits the advantages of both cloud and edge servers and
considers a Hierarchical Quantized Federated Learning (HQFL) system with one
cloud server, several edge servers and many clients, adopting a
communication-efficient training algorithm, Hier-Local-QSGD. The high
communication efficiency comes from frequent local aggregations at the edge
servers and fewer aggregations at the cloud server, as well as weight
quantization during model uploading. A tight convergence bound for non-convex
objective loss functions is derived, which is then applied to investigate two
design problems, namely, the accuracy-latency trade-off and edge-client
association. It will be shown that given a latency budget for the whole
training process, there is an optimal parameter choice with respect to the two
aggregation intervals and two quantization levels. For the edge-client
association problem, it is found that the edge-client association strategy has
no impact on the convergence speed. Empirical simulations shall verify the
findings from the convergence analysis and demonstrate the accuracy-latency
trade-off in the hierarchical federated learning system.
