We consider an asynchronous hierarchical federated learning (AHFL) setting
with a client-edge-cloud framework. The clients exchange the trained parameters
with their corresponding edge servers, which update the locally aggregated
model. This model is then transmitted to all the clients in the local cluster.
The edge servers communicate to the central cloud server for global model
aggregation. The goal of each client is to converge to the global model, while
maintaining timeliness of the clients, i.e., having optimum training iteration
time. We investigate the convergence criteria for such a system with dense
clusters. Our analysis shows that for a system of $n$ clients with fixed
average timeliness, the convergence in finite time is probabilistically
guaranteed, if the nodes are divided into $O(1)$ number of clusters, that is,
if the system is built as a sparse set of edge servers with dense client bases
each.

文章研究了一种客户端 - 边缘 - 云异步分层联邦学习的设置，通过局部聚合模型的更新并在边缘服务器之间进行交换以收敛于全局模型，最终得到一系列稠密的客户端基地。分析表明，如果将节点分成 O（1）个集群，则对于固定平均时效的 n 个客户端的系统，可以在有限时间内概率上保证收敛。