## 5 Simulations
### Simulation Results  
#### 5.2.1 Performance Comparison Among Different FL Algorithms  
Assume a deadline of \(\tau=15\) s. Figure 2 shows the learning curves for different algorithms by using MNIST. Here, Figure 2a,b show the learning curves over global iterations and time, respectively, when the data distribution is more similar to non-IID (i.e., \(\beta=0.1\)). Similarly, Figure 2c,d show the learning curves over global iterations and time, respectively, when the data distribution is more similar to IID (i.e., \(\beta=1\)). From Figure 2a,c, we can see that, in both IID (\(\beta=1\)) and non-IID (\(\beta=0.1\)) scenarios, the final model accuracy of DecantFed is slightly higher than FedAvg (which is around 90%) but much higher than FedProx, and the convergence rate over global iteration for DecantFed is slightly faster than FedAvg. The reason for having low testing accuracy for FedProx is that FedProx only selects five clients out of one hundred, and low client participation leads to an insufficient and biased training dataset, which reduces the testing accuracy of the global model. The low client participation in FedProx also results in model accuracy decreasing when the data distribution changes from IID to non-IID. Yet, the change in model accuracy over \(\beta\) for DecantFed and FedAvg is negligible because they allow all the clients to participate in the training. In Figure 2b,d, it is easy to observe that the convergence rate over time for DecantFed is much faster than FedAvg in both IID and non-IID scenarios. DecantFed is fully converged around 130,000 s achieving 90% model accuracy, while FedAvg only achieves 45% and 73% model accuracy in IID and non-IID scenarios, respectively, at 200,000 s. This is because the duration of a global iteration for FedAvg is much longer than DecantFed since FedAvg has to wait for all the clients to upload the local models.  
Figure 3 shows the learning curves for different algorithms by using CIFAR-10. We can obtain a similar conclusion in which DecantFed and FedAvg converge to a similar model test accuracy, i.e., 70% for non-IID as shown in Figure 3a and 73% for IID as shown in Figure 3c. On the other hand, FedProx only achieves 39% and 45% in non-IID and IID, respectively. This highlights that DecantFed can achieve at least 28% higher model accuracy  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Methods** & **Workload (\(d_{i}\))** & **Synchronous** & **Deadline** & **Clients** \\ \hline DecantFed & dynamic & semi-syn & \(\tau\) & all \\ \hline FedProx [20] & dynamic & syn & \(\tau\) & few \\ \hline FedAvg [3] & fixed & syn & \(\infty\) & all \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparisons of different FL algorithms.  
Figure 2: Test accuracy of different algorithms for MNIST with \(\beta=0.1\) and \(1\).  
than FedProx. Also, the convergence rate over time for DecantFed is much faster than FedAvg in both IID and non-IID scenarios, as shown in Figure 3b,d. In order to attain a test accuracy of 41%, DecantFed and FedAvg demand \(0.5\times 10^{5}\) seconds and \(2\times 10^{5}\) s, respectively. DecantFed is four times faster than FedAvg. It is worth noting that when \(\beta=0.1\) as shown in Figure 3a, the final model accuracy of FedAvg is slightly better than DecantFed, which is different from the other settings. Also, the model accuracy of FedAvg during the training is more stable than DecantFed.