## 5 Experiments
### Evaluation Using the Real Datasets  
The second set of experiments evaluated the training performance of our mechanism according to accuracy and loss when using the real datasets. We first used training loss to evaluate the performance of the three strategies. Figure 4 shows the training loss of three strategies trained with different datasets over the epochs. As training progresses, the training loss of FedNow and the two baselines both decrease with epoch, but the loss curve of FedNow clearly has the fastest decline and a faster convergence rate than the baselines. For example, in Figure 4a, when the epoch approaches 50, FedNow begins to converge, and its loss is below 0.4, while the training loss for the baselines is obviously higher than 0.4; it takes CD and UB an additional 50 and 100 epochs, respectively, to achieve a similar loss. Second, considering the fact that different strategies may have different training times in each epoch, we recorded the variation in training accuracy over time, as shown in Figure 5. Due to the ease of training with MNIST and FMNIST, the three strategies ultimately achieve similar training accuracies, as seen in Figure 5a,b; in contrast, CD achieves the highest training accuracy in Figure 5c, which may due to the fact that tending toward low-cost edge servers can motivate relatively more training samples with the same budgets. However, it is worth noting that since FedNow prioritizes selecting more efficient edge servers and allows them to personally decide their local training rounds (i.e., multiple local training rounds), the model trained with FedNow can converge over a time that is obviously shorter. For example, in FMNIST and CIFAR-10, the model trained with FedNow converges nearly 100 and 300 s earlier than CD, respectively. Moreover, CD allows multiple local training rounds but tends to choose low-cost edge servers, which leads to more training samples but also longer training times. UB requires each edge server to perform only one round of local training, which makes the overall training time under this strategy relatively short. However, this also leads to insufficient training samples/local training rounds for UB, resulting in the slowest convergence speed and the worst model accuracy. In Figure 6, in order to demonstrate the effectiveness of the efficiency-aware mechanism, we further intuitively represent the completion time when the model trained using the three strategies reaches the same accuracy. Excitingly, the completion time of FedNow is the lowest among the three training strategies. For instance, in Figure 6c, it takes 393 s, 681 s, and 801 s for a model to obtain the training accuracy of 0.75 when trained with FedNow, CD, and UB, respectively. In other words, for CIFAR10-ResNet18, FedNow saves more training time than CD and UB by as much as 42.3% and 51% when reaching an accuracy of 0.75. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Ref.** & \(\mathcal{J}^{\prime}\) & \(\mathbf{LR}\) & \(\mathbf{D}\) (\(\mathbf{\times 10^{9}}\)) & \(\mathbf{acc.l}\) (\(\mathbf{\times 10^{-2}}\)) & \(\mathbf{P}\) (\(\mathbf{\times 10^{4}}\)) & \(\mathbf{U_{S}}\) (\(\mathbf{\times 10^{-1}}\)) \\ \hline UB & \(\{1,\cdots,10\}\) & \(1\) & 10.3583 & 0.3107 & 9.2625 & 0.1152 \\ Control Group & \([1,2,3]\) & \(r_{j,j}\in\mathcal{J}^{\prime}\) & 2.4602 & 0.6375 & 6.5252 & 0.1231 \\ CD & \(\{1,2,3,4,5\}\) & \(r_{j},j\in\mathcal{J}^{\prime}\) & 7.5857 & 0.363 & 7.5447 & 0.1048 \\ MEC & \(\{1,3,5,10\}\) & \(r_{j,j}\in\mathcal{J}^{\prime}\) & 10.4166 & 0.3098 & 7.0024 & 0.0946 \\ FedNow & \(\{1,2,3,10\}\) & \(r_{j,j}\in\mathcal{J}^{\prime}\) & 9.0836 & 0.3317 & 7.4569 & 0.1009 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Differences in performance for different metric; \(LR\) means the local training rounds, and \(D\) denotes the overall data size contributed by the incentivized set \(\mathcal{J}^{\prime}\). Figure 4: Training loss for the three strategies with epoch. (**a**) MNIST-MLP; (**b**) FMNIST-CNN; (**c**) CIFAR10-Resnet18.