###### Abstract
The other solution to solve the straggler problem is to apply asynchronous FL, where the FL server does not need to wait until the deadline expires for each global iteration but would update the global model once it receives a local model from a client [15]. However, the asynchronous FL may suffer from (1) the high communications cost since both the FL server and clients will more frequently exchange their models and (2) the stale issue, where some slow clients are training based on an outdated global model, which may lead to slow convergence rate or even global model divergence [16; 17]. To solve the slow convergence and model overfitting issues in the synchronous FL while avoiding model divergence in the asynchronous FL, we propose a semi-synchronous FL method, i.e., Latency awarE Semi-synchronous client Selection and mOdel aggregation  
Figure 1: Wireless federated learning. for federated learNing (LESSON). The basic idea of LESSON is to allow all the clients to participate in the whole learning process with different frequencies. Specifically, the clients are clustered into different tiers based on their model training and uploading latency. The clients in a lower tier (i.e., lower model training and uploading latency) would participate in the learning process more frequently than those in a higher tier (with higher model training and uploading latency). As a result, the straggler problem can be resolved (since the FL server does not need to wait for stragglers in each global iteration), and the model overfitting problem can be fixed (since all the clients join the learning process to provide high data diversity). The main contributions of the paper are summarized as follows. 1. A new semi-synchronous FL algorithm, i.e., LESSON, is introduced. LESSON introduces a latency-aware client clustering technique that groups clients into different tiers based on their computing and uploading latency. LESSON allows all the clients in the system to participate in the training process but at different frequencies, depending on the clients' associated tiers. LESSON is expected to mitigate the straggler problem in synchronous FL and model overfitting in asynchronous FL, thus expediting model convergence. 2. LESSON also features a specialized model aggregation method tailored to client clustering. This method sets the weight and timing for local model aggregation for each client tier. 3. The proposed LESSON algorithm also integrates the dynamic model aggregation and step size adjustment according to client clustering and offers flexibility in balancing model accuracy and convergence speed by adjusting the deadline \(\tau\). 4. Extensive experimental evaluations show that LESSON outperforms FedAvg and FedCS in terms of faster convergence and higher model accuracy. The rest of this paper is organized as follows. The related work is summarized in Section 2. System models are described in Section 3. Section 4 elaborates on the proposed LESSON algorithm, which comprises client clustering and model aggregation. In Section 5, the performance of LESSON is compared with the other two baseline algorithms via extensive simulations, and simulation results are analyzed. Finally, Section 6 concludes this paper.