  To exploit massive amounts of data generated at mobile edge networks,
federated learning (FL) has been proposed as an attractive substitute for
centralized machine learning (ML). By collaboratively training a shared
learning model at edge devices, FL avoids direct data transmission and thus
overcomes high communication latency and privacy issues as compared to
centralized ML. To improve the communication efficiency in FL model
aggregation, over-the-air computation has been introduced to support a large
number of simultaneous local model uploading by exploiting the inherent
superposition property of wireless channels. However, due to the heterogeneity
of communication capacities among edge devices, over-the-air FL suffers from
the straggler issue in which the device with the weakest channel acts as a
bottleneck of the model aggregation performance. This issue can be alleviated
by device selection to some extent, but the latter still suffers from a
tradeoff between data exploitation and model communication. In this paper, we
leverage the reconfigurable intelligent surface (RIS) technology to relieve the
straggler issue in over-the-air FL. Specifically, we develop a learning
analysis framework to quantitatively characterize the impact of device
selection and model aggregation error on the convergence of over-the-air FL.
Then, we formulate a unified communication-learning optimization problem to
jointly optimize device selection, over-the-air transceiver design, and RIS
configuration. Numerical experiments show that the proposed design achieves
substantial learning accuracy improvement compared with the state-of-the-art
approaches, especially when channel conditions vary dramatically across edge
devices.
