Federated learning has gained popularity as a means of training models distributed across the wireless edge. The paper introduces delay-aware hierarchical federated learning (DFL) to improve the efficiency of distributed machine learning (ML) model training by accounting for communication delays between edge and cloud. Different from traditional federated learning, DFL leverages multiple stochastic gradient descent iterations on local datasets within each global aggregation period and intermittently aggregates model parameters through edge servers in local subnetworks. During global synchronization, the cloud server consolidates local models with the outdated global model using a local-global combiner, thus preserving crucial elements of both, enhancing learning efficiency under the presence of delay. A set of conditions is obtained to achieve the sub-linear convergence rate of O(1/k) for strongly convex and smooth loss functions. Based on these findings, an adaptive control algorithm is developed for DFL, implementing policies to mitigate energy consumption and communication latency while aiming for sublinear convergence. Numerical evaluations show DFL's superior performance in terms of faster global model convergence, reduced resource consumption, and robustness against communication delays compared to existing FL algorithms. In summary, this proposed method offers improved efficiency and results when dealing with both convex and non-convex loss functions.

翻译：联邦学习作为在无线边缘分布式训练模型的方法已受到广泛关注。本文提出延迟感知的层次化联邦学习（DFL），通过考虑边缘与云之间的通信延迟，提升分布式机器学习模型训练的效率。与传统联邦学习不同，DFL在每个全局聚合周期内，利用本地数据集执行多次随机梯度下降迭代，并通过边缘服务器在局部子网中间歇性聚合模型参数。在全局同步过程中，云服务器利用本地-全局组合器将局部模型与过时的全局模型进行整合，从而保留两者的关键要素，在延迟存在时提升学习效率。针对强凸且平滑的损失函数，本文推导了实现次线性收敛速度O(1/k)的条件。基于这些发现，为DFL开发了自适应控制算法，实施策略以降低能耗和通信延迟，同时追求次线性收敛。数值评估表明，与现有联邦学习算法相比，DFL在更快的全局模型收敛速度、更低的资源消耗以及对通信延迟的鲁棒性方面表现出优越性能。总之，所提方法在处理凸与非凸损失函数时均能提升效率与性能。