This paper investigates an over-the-air federated learning (OTA-FL) system that employs fluid antennas (FAs) at an access point. The system enhances learning performance by leveraging the additional degrees of freedom provided by antenna mobility. We analyze the convergence of the OTA-FL system and derive the optimality gap to illustrate the influence of FAs on learning performance. With these results, we formulate a nonconvex optimization problem to minimize the optimality gap by jointly optimizing the positions of the FAs, the beamforming vector, and the transmit power allocation at each user. To address the dynamic environment, we cast this optimization problem as a Markov decision process and propose the recurrent 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

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