  This paper studies the design of wireless federated learning (FL) for
simultaneously training multiple machine learning models. We consider round
robin device-model assignment and downlink beamforming for concurrent multiple
model updates. After formulating the joint downlink-uplink transmission
process, we derive the per-model global update expression over communication
rounds, capturing the effect of beamforming and noisy reception. To maximize
the multi-model training convergence rate, we derive an upper bound on the
optimality gap of the global model update and use it to formulate a multi-group
multicast beamforming problem. We show that this problem can be converted to
minimizing the sum of inverse received signal-to-interference-plus-noise
ratios, which can be solved efficiently by projected gradient descent.
Simulation shows that our proposed multi-model FL solution outperforms other
alternatives, including conventional single-model sequential training and
multi-model zero-forcing beamforming.
