  To efficiently exploit the massive amounts of raw data that are increasingly
being generated in mobile edge networks, federated learning (FL) has emerged as
a promising distributed learning technique. By collaboratively training a
shared learning model on edge devices, raw data transmission and storage are
replaced by the exchange of the local computed parameters/gradients in FL,
which thus helps address latency and privacy issues. However, the number of
resource blocks when using traditional orthogonal transmission strategies for
FL linearly scales with the number of participating devices, which conflicts
with the scarcity of communication resources. To tackle this issue,
over-the-air computation (AirComp) has emerged recently which leverages the
inherent superposition property of wireless channels to perform one-shot model
aggregation. However, the aggregation accuracy in AirComp suffers from the
unfavorable wireless propagation environment. In this paper, we consider the
use of intelligent reflecting surfaces (IRSs) to mitigate this problem and
improve FL performance with AirComp. Specifically, a performance-oriented
design scheme that directly minimizes the optimality gap of the loss function
is proposed to accelerate the convergence of AirComp-based FL. We first analyze
the convergence behavior of the FL procedure with the absence of channel fading
and noise. Based on the obtained optimality gap which characterizes the impact
of channel fading and noise in different communication rounds on the ultimate
performance of FL, we propose both online and offline approaches to tackle the
resulting design problem. Simulation results demonstrate that such a
performance-oriented design strategy can achieve higher test accuracy than the
conventional isolated mean square error (MSE) minimization approach in FL.
