This paper investigates over-the-air model aggregation for distributed reconfigurable intelligent surfaces (RISs)-assisted federated learning systems. Specifically, channel state information at the senors is assumed to be unavailable to avoid the overwhelming feedback overhead. With the objective of computation distortion minimization, we jointly optimize distributed RIS reflection matrices and the receiver beamforming, subject to the unit-modulus constraints imposed on the RIS reflection coefficients. In order to tackle this non-convex design problem, an alternating-based algorithm is proposed where, at every step, the RIS reflection matrices and the receiver beamforming are both obtained in closed forms. Numerical results validate the effectiveness of the proposed algorithm in reducing the aggregation error.

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