# Personalized Federated Learning with Progressive Local Training Strategy and Lightweight Classifier
## 4 Experiments
### A Comparison with State-of-the-Art Methods  
To validate the effectiveness of our method, we compared it with several state-of-the-art methods in the field of federated learning and conducted a comprehensive evaluation. We used \(P\) to represent the proportion of clients participating in training each round. The smaller the \(P\), the fewer clients participated in training, increasing the likelihood of clients being offline for extended periods. In our experiments, we set \(P\) to [0.3, 0.5, 0.7] to simulate collaborative training scenarios under different participation rates. This variation in participation rates helped us understand how our method performs under different levels of client availability. Additionally, for the Dirichlet partitioning method, the smaller the \(\beta\), the greater the degree of data heterogeneity. We set \(\beta\) to [0.1, 0.3, 0.5] to simulate different levels of data heterogeneity using Dirichlet partitioning methods. These parameter settings effectively simulated environments with high data heterogeneity at different participation rates, allowing us to thoroughly evaluate the robustness of our method. For the pathological Non-IID partitioning method, we set the number of classes to 5 for cifar10 and 30 for cifar100. This approach involved dividing the dataset into multiple small shards and randomly assigning these shards to different clients, resulting in significant heterogeneity in the data distribution across clients. This setup was designed to mimic real-world scenarios where data distributions can vary widely among different clients. Extensive experiments were conducted in the above simulated environments. The results are shown in Tables 2-4. We report the accuracy of different methods on the cifar10 and cifar100 datasets under various conditions. These tables provide a comprehensive comparison of our method against existing approaches, highlighting its effectiveness in handling data heterogeneity and varying participation rates. In Table 2, we show the experimental results in the case where the dataset was cifar10 and the data partitioning method was Dirichlet partitioning. Notably, when \(\beta\) = 0.5 and \(P\) = 0.3, PFPS-LWC surpassed the baseline by an impressive 4.18%. Moreover, PFPS-LWC achieved optimal performance in all settings, compared to other methods. When the dataset was cifar100, with \(\beta\) = 0.1 and \(P\) = 0.5, as shown in Table 3, our method surpassed the baseline by an impressive 4.03%. This significant improvement highlights the effectiveness of our approach in scenarios with strong data heterogeneity and lower client participation rates. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{5}{c}{**Accuracy\(\dagger\) Predicted with Different Settings of \(\beta\) and \(P\) on Cifar10**.} \\ \cline{2-9}  & \multicolumn{2}{c}{\(\beta=\mathbf{0.1}\)} & \multicolumn{2}{c}{\(\beta=\mathbf{0.3}\)} & \multicolumn{2}{c}{\(\beta=\mathbf{0.5}\)} \\ \cline{2-9}  & \(P=\mathbf{0.3}\) & \(P=\mathbf{0.5}\) & \(P=\mathbf{0.7}\) & \(P=\mathbf{0.3}\) & \(P=\mathbf{0.5}\) & \(P=\mathbf{0.7}\) & \(P=\mathbf{0.3}\) & \(P=\mathbf{0.5}\) & \(P=\mathbf{0.7}\) \\ \hline FedAvg [29] & 33.03 & 34.54 & 52.3 & 49.17 & 56.5 & 58.95 & 56.15 & 56.36 & 54.14 \\ FedProx [14] & 36.35 & 40.03 & 53.84 & 52.59 & 58.79 & 59.2 & 57.34 & 58.67 & 56.86 \\ FedPer [20] & 89.36 & 87.09 & 87.48 & 79.74 & 79.01 & 79.94 & 75.59 & 76.21 & 76.4 \\ pFedMe [37] & 87.68 & 86.08 & 86.04 & 77.59 & 75.73 & _69.67_ & 70.8 & 71.8 & 71.16 \\ FedBN [23] & 67.91 & 84.66 & 85.29 & 72.72 & 74.61 & 73.85 & 70.27 & 72.41 & 72.96 \\ FedProx [41] & 88.56 & 88.42 & 89.11 & 76.96 & 77.71 & 77.08 & 72.31 & 72.15 & 72.36 \\ PFPS-LWC & 90.58 & 91.03 & 90.91 & 82.36 & 82.81 & 83.18 & 79.77 & 80.43 & 80.33 \\ \(\Delta\) & **1.22** & **3.94** & **3.43** & **2.62** & **3.8** & **3.24** & **4.18** & **4.22** & **3.93** \\ \hline \hline \end{tabular}
\end{table}