## 2 Related Work  
Solving the straggler issue is one of the main challenges in synchronous FL. The existing solutions mainly focus on jointly optimizing client selection and resource allocation. [PERSON] and [PERSON] [18] aimed to maximize the number of selected clients that can finish their model training and uploading before a predefined deadline in each global iteration. By assuming that the selected clients must iteratively upload their models to the FL server, they designed FedCS that jointly optimizes the uploading schedule and client selection to achieve the objective. [PERSON] and [PERSON] [19] designed a similar client selection method FedMCCS. The goal of FedMCCS is to maximize the number of selected clients who can not only finish the model training and uploading before a predefined deadline but also guarantee the resource utilization is less than the threshold to avoid device dropout. [PERSON] et al. [11] proposed a client selection method that tries to achieve the same objective as FedCS, but they argued that the latency of a client in waiting for the wireless channel to be available for model uploading should be considered; otherwise, the selected clients may not upload their local models before the deadline. [PERSON] et al. [20] proposed to dynamically adjust and optimize the trade-off between maximizing the number of selected clients and minimizing the total energy consumption of the selected clients by picking suitable clients and allocating appropriate resources (in terms of CPU frequency and transmission power) in each global iteration. [PERSON] et al. [21] also jointly optimized the client selection and resource allocation for FL. However, the objective is to minimize the overall learning latency (which equals the product of the average latency of one global iteration and the number of global iterations) while achieving a certain model accuracy. They formulated a system model to estimate the number of global iterations given the global model accuracy requirement. All the mentioned client selection methods for synchronous FL can alleviate the straggler problem but may lead to a slow convergence rate and model overfitting issues, as we illustrated previously. Instead of selecting qualified clients to avoid stragglers, [PERSON] et al. [22] proposed to let fast clients train their local models by running more gradient descent iterations in each global iteration. In this way, the fast and slow clients could upload their models at a similar time, but the fast clients may provide better models to fit their local data samples, thus potentially speeding up the model convergence. This method, however, may lead to local model overfitting issues when some fast clients run too many gradient descent iterations over the limited data samples. The overfitted local models would significantly slow down the global model convergence. [PERSON] et al. [23] proposed to perform spilt learning, where a global neural network is divided into two parts. The parameters in the former and latter layers are trained in the clients and the FL server, respectively. As a result, the computational complexity of the clients is reduced, thus potentially reducing the training time and energy consumption of the clients. Other works aim to design asynchronous FL, where the FL server does not need to wait for the selected clients to upload their local models; instead, once the FL server receives a local model from a client, it would aggregate the received local model to update the global model, and then send the updated global model to the client [24; 25; 26; 27]. However, as mentioned before, the fast clients and the FL server must exchange their models more frequently, thus leading to higher communications costs for both the fast clients and FL server [28; 29]. Meanwhile, in asynchronous FL, the slower clients may train their local models based on an outdated global model, which results in slow convergence or even leads to model divergence [30; 31].