-1To 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. 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 novel performance-oriented long-term design scheme that integrated design multiple communication rounds to minimize the optimality gap of the loss function is proposed. 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 schemes to tackle the resulting design problem. Simulation results demonstrate that such a long-term design strategy can achieve higher test accuracy than the conventional isolated design approach in FL. Both the theoretical analysis and numerical results exhibit a “later-is-better” principle, which demonstrates the later rounds in the FL procedure are more sensitive to aggregation error, and hence more resources are required over time.