Energy Minimization for Federated Learning with IRS-Assisted Over-the-Air Computation

This paper investigates the deployment of federated learning (FL) over an over-the-air computation (AirComp) and intelligent reflecting surface (IRS) based wireless network. In the considered system, devices transmit locally trained machine learning (ML) models to the base station (BS) which aggregates the received ML models and generates a shared global ML model. The devices can directly transmit ML models to the BS or using IRS. Meanwhile, AirComp is used to aggregate ML models that are transmitted from the devices to the BS. To minimize the energy consumption of devices, an energy minimization problem is formulated, which jointly optimizes the device selection, phase shift matrix, decoding vector, and power control. To seek the solution, the original optimization problem is divided into four sub-problems. Then the fractional program, greedy algorithm, matrix derivation, and weighted minimum mean square error methods are used to compute the phase shift matrix, device selection vector, decoding vector, and transmit power, respectively. Simulation results show that the proposed algorithm can reduce 11.2% energy consumption of devices compared to an FL algorithm that is implemented at a network without any IRSs.