The paradigm of federated learning (FL) to address data privacy concerns by locally training parameters on resource-constrained clients in a distributed manner has garnered significant attention. Nonetheless, FL is not applicable when not all clients within the coverage of the FL server are registered with the FL network. To bridge this gap, this paper proposes joint learner referral aided federated client selection (LRef-FedCS), along with communications and computing resource scheduling, and local model accuracy optimization (LMAO) methods. These methods are designed to minimize the cost incurred by the worst-case participant and ensure the long-term fairness of FL in hierarchical Internet of Things (HieIoT) networks. Utilizing the Lyapunov optimization technique, we reformulate the original problem into a stepwise joint optimization problem (JOP). Subsequently, to tackle the mixed-integer non-convex JOP, we separatively and iteratively address LRef-FedCS and LMAO through the centralized method and self-adaptive global best harmony search (SGHS) algorithm, respectively. To enhance scalability, we further propose a distributed LRef-FedCS approach based on a matching game to replace the centralized method described above. Numerical simulations and experimental results on the MNIST/CIFAR-10 datasets demonstrate that our proposed LRef-FedCS approach could achieve a good balance between pursuing high global accuracy and reducing cost.

翻译：联邦学习（FL）范式通过以分布式方式在资源受限的客户端本地训练参数来应对数据隐私问题，已引起广泛关注。然而，当FL服务器覆盖范围内的所有客户端并未全部注册到FL网络时，FL便无法适用。为弥补这一不足，本文提出了一种联合学习者推荐辅助的联邦客户端选择（LRef-FedCS）方法，并结合通信与计算资源调度及本地模型精度优化（LMAO）方法。这些方法旨在最小化最差参与者的成本，并确保分层物联网（HieIoT）网络中FL的长期公平性。利用Lyapunov优化技术，我们将原问题重新表述为逐步联合优化问题（JOP）。随后，为解决混合整数非凸JOP，我们分别通过集中式方法和自适应全局最佳和声搜索（SGHS）算法迭代处理LRef-FedCS与LMAO。为提升可扩展性，我们进一步提出一种基于匹配博弈的分布式LRef-FedCS方法，以替代上述集中式方法。在MNIST/CIFAR-10数据集上的数值仿真与实验结果表明，所提出的LRef-FedCS方法能够在追求高全局精度与降低成本之间实现良好平衡。