Energy-Efficient and Fast Controlled Descent for Over-the-Air Assisted Federated Learning

We propose a novel energy-efficient controlled descent algorithm (EECDA) for over-the-air computation-assisted federated learning. In EECDA, the computing devices transmit their local parameters to the parameter server using amplitude modulation over a common time-frequency resource. As a result, a computation that involves adding the data of multiple users occurs automatically over the wireless channel since the signals superimpose. EECDA adapts the transmit powers of the devices and the amplification at the receiver to minimize the error floor on the optimality gap, which measures the performance of the federated learning algorithm. We derive the transmit powers and receiver amplification in closed-form. This is based on a novel recursive upper bound on the optimality gap that characterizes how wireless channel fades, device transmit powers, receiver amplification, noise variance, and batch selection variance determine the effective learning rate and error floor. For a small total energy, EECDA achieves a markedly lower optimality gap than the conventional minimum mean square error scheme.