Over-the-air federated learning (OTA-FL) integrates communication and model aggregation by exploiting the innate superposition property of wireless channels. The approach renders bandwidth efficient learning, but requires care in handling the wireless physical layer impairments. In this paper, federated edge learning is considered for a network that is heterogeneous with respect to client (edge node) data set distributions and individual client resources, under a general non-convex learning objective. We augment the wireless OTA-FL system with a Reconfigurable Intelligent Surface (RIS) to enable a propagation environment with improved learning performance in a realistic time varying physical layer. Our approach is a cross-layer perspective that jointly optimizes communication, computation and learning resources, in this general heterogeneous setting. We adapt the local computation steps and transmission power of the clients in conjunction with the RIS phase shifts. The resulting joint communication and learning algorithm, RIS-assisted Over-the-air Adaptive Resource Allocation for Federated learning (ROAR-Fed) is shown to be convergent in this general setting. Numerical results demonstrate the effectiveness of ROAR-Fed under heterogeneous (non i.i.d.) data and imperfect CSI, indicating the advantage of RIS assisted learning in this general set up.

翻译：空中联邦学习（OTA-FL）通过利用无线信道的固有叠加特性，将通信与模型聚合过程相结合。该方法可在实现带宽高效学习的同时，需谨慎处理无线物理层损伤问题。本文针对客户端（边缘节点）数据集分布与个体资源均存在异质性的网络，在非凸学习目标下研究联邦边缘学习。我们为无线OTA-FL系统引入可重构智能表面（RIS），以在时变物理层环境中构建传播环境，从而提升学习性能。本方法采用跨层视角，在异质性场景中联合优化通信、计算与学习资源。我们根据RIS相位偏移自适应调整客户端的本地计算步数与发射功率。所提出的联合通信与学习算法——面向联邦学习的RIS辅助空中自适应资源分配（ROAR-Fed）——在该通用场景下被证明具有收敛性。数值结果表明，ROAR-Fed在异质（非独立同分布）数据与非完美信道状态信息条件下均具有有效性，充分展示了RIS辅助学习在该通用框架下的优势。