  Over-the-air federated learning (OTA-FL) provides bandwidth-efficient
learning by leveraging the inherent superposition property of wireless
channels. Personalized federated learning balances performance for users with
diverse datasets, addressing real-life data heterogeneity. We propose the first
personalized OTA-FL scheme through multi-task learning, assisted by personal
reconfigurable intelligent surfaces (RIS) for each user. We take a cross-layer
approach that optimizes communication and computation resources for global and
personalized tasks in time-varying channels with imperfect channel state
information, using multi-task learning for non-i.i.d data. Our PROAR-PFed
algorithm adaptively designs power, local iterations, and RIS configurations.
We present convergence analysis for non-convex objectives and demonstrate that
PROAR-PFed outperforms state-of-the-art on the Fashion-MNIST dataset.
