  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.
