Robust transmission design for federated learning through over-the-air computation

Over-the-air computation (AirComp) enables federated learning (FL) to rapidly aggregate local models at the central server using waveform superposition property of wireless channel. In this paper, a robust transmission scheme for an AirComp-based FL system with imperfect channel state information (CSI) is proposed. To model CSI uncertainty, an expectation-based error model is utilized. The main objective is to maximize the number of selected devices that meet mean-squared error (MSE) requirements for model broadcast and model aggregation. The problem is formulated as a combinatorial optimization problem and is solved in two steps. First, the priority order of devices is determined by a sparsity-inducing procedure. Then, a feasibility detection scheme is used to select the maximum number of devices to guarantee that the MSE requirements are met. An alternating optimization (AO) scheme is used to transform the resulting nonconvex problem into two convex subproblems. Numerical results illustrate the effectiveness and robustness of the proposed scheme.