# Communication-Efficient Federated Learning with Adaptive Consensus ADMM
## 5 Experiments
### Comparison with Other Baselines  
Comparing the proposed algorithm with existing mainstream federal optimization methods is crucial for assessing model performance. However, due to the constraints of the current communication channels, reducing the communication overhead has remained a challenge for FL. Therefore, it is reasonable to anticipate that the proposed algorithm would minimize the number of communication rounds while maintaining good heterogeneity. In the ensuing comparative experiments, we aim to contrast the performance of FedACADMM against that of FedAvg and FedProx. Specifically, we investigate their efficacy across three extensive empirical datasets, various data distribution techniques, and diverse client numbers. Our experiments generated promising results, which was really exciting. Table 4 shows the communication rounds required to accomplish the test target accuracy under various conditions. In Table 4, we report the number of communication rounds required by each of the three algorithms to attain the target accuracy for three distinct datasets, varying data distributions, and a range of client population sizes. Additionally, we provide a graphical representation of the results in Figure 3, which facilitates a more insightful interpretation of the outcomes. The statistics of communication reduction by FedACADMM over FedAvg are shown in Table 5. It can be observed that in most circumstances, the suggested algorithm FedACADMM can require less rounds than the baselines to attain the test target accuracy. To visually communicate our experimental findings, we have chosen to present a selection of representative results as images, as shown in Figure 4.  
Figure 2: Choice of the initial variable parameter \(\rho^{0}\). This method provides a clear and concise representation of the data. In Figure 4a-d, the experimental results of each algorithm in the FMNIST dataset and the data distribution of IID are shown with different numbers of clients. We can observe that the performances of the three algorithms are quite good under homogeneous conditions, and the test accuracy of FedACADMM is slightly better than the other two algorithms. In Figure 4i-l, the experimental results of each algorithm in the CIFAR-10 dataset and the data distribution of non-IID are shown with different numbers of clients. When the number of clients is small, the test accuracy of FedACADMM is almost the same as that of the other two algorithms, but its advantage becomes obvious as the number of clients increases; as such, we guess that it is suitable for large-scale communication. In Figure 4e-h, the experimental results of each algorithm in the FMNIST dataset and the data distribution of non-IID are shown with different numbers of clients. It will not be repeated because its experimental results are similar to those of the CIFAR-10 dataset. In Figure 5, the corresponding train loss of test accuracy in Figure 4 is shown, and it can be seen that the convergence performance of FedACADMM is equal to the other two algorithms in most heterogeneous cases, and the convergence speed can be better than the other two algorithms in homogeneous cases. In Figure 6, we selectively display the  
Through the detailed analysis above, we can see some advantages of FedACADMM:  
**Communication efficiency. ** Under the homogeneous data distribution method, almost all experimental methods can quickly achieve the test target accuracy, and the increase in the number of clients enables the advantages of our proposed method to be reflected. However, a homogeneous experimental setup is not informative for real-life situations. On the other hand, in a heterogeneous experimental environment, the proposed method gradually exhibits robustness with the complexity of the environment. Our proposed method successfully handles the client drift problem in diverse environments and is optimized for the local training problem. **Data Heterogeneity.