## 8 Simulations
### Simulation Results
Pairing  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**MNIST**} \\ \hline  & \multicolumn{2}{c}{**Target Accuracy—95\%**} & \multicolumn{2}{c}{**Target Accuracy—96\%**} & \multicolumn{2}{c}{**Target Accuracy—97\%**} & \multicolumn{2}{c}{**Target Accuracy—98\%**} & \multicolumn{2}{c}{**Highest Accuracy**} \\  & \multicolumn{2}{c}{**TD**} & \multicolumn{2}{c}{**EC**} & \multicolumn{2}{c}{**TD**} & \multicolumn{2}{c}{**EC**} & \multicolumn{2}{c}{**TD**} & \multicolumn{2}{c}{**EC**} & \multicolumn{2}{c}{**TD**} & \multicolumn{2}{c}{**EC**} \\ \hline Method 1 & 164 & 1343 & 211 & 1819 & **444** & 3462 & 748 & 6435 & 0.9859 \\ Method 2 & 182 & 1239 & 276 & 1962 & 453 & **3099** & 981 & 6954 & 0.9828 \\ Method 3 & 296 & 1632 & 371 & 2138 & 569 & 3423 & - & - & 0.9808 \\ Method 4 & 255 & 1514 & 291 & 1738 & 509 & 2991 & 1034 & 6279 & 0.9827 \\ Method 5 & 212 & 1427 & 315 & 2182 & 518 & 3549 & 979 & 7028 & 0.9839 \\ Method 6 & 177 & 1122 & 256 & 1629 & 493 & 3418 & 831 & 6315 & 0.9857 \\ Proposed & **139** & **1046** & **174** & **1311** & **444** & 3307 & **627** & **5085** & **0.9865** \\ \hline \hline \multicolumn{10}{c}{**CIFAR10**} \\ \hline  & \multicolumn{2}{c}{**Target Accuracy—80\%**} & \multicolumn{2}{c}{**Target Accuracy—85\%**} & \multicolumn{2}{c}{**Target Accuracy—87\%**} & \multicolumn{2}{c}{**Target Accuracy—88\%**} & \multicolumn{2}{c}{**Highest Accuracy**} \\  & \multicolumn{2}{c}{**TD**} & \multicolumn{2}{c}{**EC**} & \multicolumn{2}{c}{**TD**} & \multicolumn{2}{c}{**EC**} & \multicolumn{2}{c}{**TD**} & \multicolumn{2}{c}{**EC**} \\ \hline Method 1 & 33,003 & 302,417 & 77,411 & 720,087 & 132,883 & 1,233,245 & 179,835 & 1,668,598 & 0.8808 \\ Method 2 & 56,067 & 425,742 & 101,316 & 771,132 & 178,139 & 1,363,374 & - & - & 0.8707 \\ Method 3 & 50,954 & 340,572 & 96,168 & 660,553 & - & - & - & - & 0.8635 \\ Method 4 & 50,973 & 340,210 & 134,439 & 787,462 & - & - & - & - & 0.8613 \\ Method 5 & 42,411 & 286,778 & 101,314 & 674,537 & 159,341 & 1,078,677 & - & - & 0.8710 \\ Method 6 & 38,169 & 271,664 & 95,652 & 643,017 & 1,612,855 & 1,065,241 & 153,328 & 1,459,732 & 0.8804 \\ Proposed & **27,911** & **252,493** & **66,315** & **601,482** & **108,145** & **972,479** & **131,176** & **1,123,961** & **0.8843** \\ \hline \hline \multicolumn{10}{c}{**FashionMNIST**} \\ \hline  & \multicolumn{2}{c}{**Target Accuracy—80\%**} & \multicolumn{2}{c}{**Target Accuracy—85\%**} & \multicolumn{2}{c}{**Target Accuracy—87\%**} & \multicolumn{2}{c}{**Target Accuracy—88\%**} & \multicolumn{2}{c}{**Highest Accuracy**} \\  & \multicolumn{2}{c}{**TD**} & \multicolumn{2}{c}{**EC**} & \multicolumn{2}{c}{**TD**} & \multicolumn{2}{c}{**EC**} & \multicolumn{2}{c}{**TD**} & \multicolumn{2}{c}{**EC**} \\ \hline Method 1 & 2769 & 25,256 & 6001 & 54,454 & 10,464 & 96,068 & **14,934** & 137,331 & 0.8865 \\ Method 2 & 3486 & 25,879 & 6626 & 49,244 & 11,516 & 86,231 & 17,402 &  
based solely on similarity can result in significant differences in computing capability within each edge, leading to more model parameter loss when using dropout for enforced synchronization, making it unsuitable for heterogeneous client scenarios. The proposed method outperforms the other three pairing methods. Finally, an ablation experiment is conducted on the reward-penalty factor strategy, primarily comparing the scenarios of not using reward-penalty factors and using the reward-penalty factors in reverse (i.e., swapping \(\chi_{i}\) and \(\xi_{i}\)). The results on the MNIST dataset are shown in Figure 6. It can be observed that the overall effect of using the reward-penalty factors is the best, while the methods of not using them and using them in reverse show slightly worse performance. The reason the method without reward-penalty factors performs slightly worse is that it fails to fully integrate heterogeneous computing capabilities into the contribution evaluation. Without this consideration, the performance is diminished in scenarios with heterogeneous clients.