  This letter investigates an over-the-air federated learning (OTA-FL) system
that employs fluid antennas (FAs) at the access point (AP) to enhance learning
performance by leveraging the additional degrees of freedom provided by antenna
mobility. First, we analyze the convergence of the OTA-FL system and derive the
optimality gap to illustrate the influence of FAs on learning performance.
Then, we formulate a nonconvex optimization problem to minimize the optimality
gap by jointly optimizing the positions of the FAs and the beamforming vector.
To address the dynamic environment, we cast this optimization problem as a
Markov decision process (MDP) and propose the recurrent deep deterministic
policy gradient (RDPG) algorithm. Finally, extensive simulations show that the
FA-assisted OTA-FL system outperforms systems with fixed-position antennas and
that the RDPG algorithm surpasses the existing methods.
