Under the organization of the base station (BS), wireless federated learning (FL) enables collaborative model training among multiple devices. However, the BS is merely responsible for aggregating local updates during the training process, which incurs a waste of the computational resource at the BS. To tackle this issue, we propose a semi-federated learning (SemiFL) paradigm to leverage the computing capabilities of both the BS and devices for a hybrid implementation of centralized learning (CL) and FL. Specifically, each device sends both local gradients and data samples to the BS for training a shared global model. To improve communication efficiency over the same time-frequency resources, we integrate over-the-air computation for aggregation and non-orthogonal multiple access for transmission by designing a novel transceiver structure. To gain deep insights, we conduct convergence analysis by deriving a closed-form optimality gap for SemiFL and extend the result to two extra cases. In the first case, the BS uses all accumulated data samples to calculate the CL gradient, while a decreasing learning rate is adopted in the second case. Our analytical results capture the destructive effect of wireless communication and show that both FL and CL are special cases of SemiFL. Then, we formulate a non-convex problem to reduce the optimality gap by jointly optimizing the transmit power and receive beamformers. Accordingly, we propose a two-stage algorithm to solve this intractable problem, in which we provide the closed-form solutions to the beamformers. Extensive simulation results on two real-world datasets corroborate our theoretical analysis, and show that the proposed SemiFL outperforms conventional FL and achieves 3.2% accuracy gain on the MNIST dataset compared to state-of-the-art benchmarks.

翻译：在基站（BS）的组织下，无线联邦学习（FL）实现了多设备间的协同模型训练。然而，基站仅负责训练过程中的本地更新聚合，导致其计算资源被浪费。为解决此问题，我们提出半联邦学习（SemiFL）范式，通过利用基站与设备的计算能力，实现集中式学习（CL）与FL的混合实施。具体而言，每个设备同时向基站发送本地梯度与数据样本以训练共享的全局模型。为在同一时频资源上提升通信效率，我们通过设计新型收发机结构，融合了用于聚合的空中计算与非正交多址接入技术。为深入理解，我们通过推导SemiFL的闭式最优性间隙进行收敛性分析，并将结果推广至两种额外情形：第一种情形中，基站使用所有累积数据样本计算CL梯度；第二种情形则采用递减学习率。我们的分析结果揭示了无线通信的有害影响，并表明FL与CL均为SemiFL的特殊情况。随后，我们构建了一个非凸问题，通过联合优化发射功率与接收波束赋形器来减小最优性间隙。据此，我们提出一种两阶段算法求解该棘手问题，并给出了波束赋形器的闭式解。基于两个真实数据集的广泛仿真结果验证了我们的理论分析，并表明所提SemiFL优于传统FL，在MNIST数据集上相比现有最优基准实现了3.2%的准确率提升。