# Personalized Federated Learning with Progressive Local Training Strategy and Lightweight Classifier
## 4 Experiments
### A Comparison with State-of-the-Art Methods
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{4}{c}{**Accuracy\(\dagger\) Predicted with Different Settings of \(\beta\) and \(P\) on Cifar100**} \\ \cline{2-10}  & \multicolumn{2}{c}{\(\beta=0.1\)} & \multicolumn{2}{c}{\(\beta=0.3\)} & \multicolumn{2}{c}{\(\beta=0.5\)} \\ \cline{2-10}  & \(P=0.3\) & \(P=0.5\) & \(P=0.7\) & \(P=0.3\) & \(P=0.5\) & \(P=0.7\) & \(P=0.3\) & \(P=0.5\) & \(P=0.7\) \\ \hline FedAvg [29] & 18.68 & 21.22 & 23.64 & 22.81 & 25.55 & 26.73 & 24.05 & 25.6 & 27.76 \\ FedProx [14] & 19.5 & 22.03 & 24.31 & 23.45 & 25.72 & 24.77 & 23.78 & 26.11 & 27.25 \\ FedPer [20] & 43.18 & 43.97 & 44.92 & 37.57 & 37.55 & 36.71 & 31.23 & 31.05 & 31.32 \\ pFedMe [37] & 28.89 & 34.98 & 34.04 & 22.34 & 24.41 & 24.58 & 19.01 & 20.84 & 21.19 \\ FedBN [23] & 21.17 & 26.88 & 29.57 & 25.71 & 30.05 & 32.03 & 28.36 & 31.45 & 32.51 \\ FedProto [41] & 35.57 & 34.31 & 35.43 & 20.66 & 21.5 & 21.18 & 13.14 & 13.27 & 13.8 \\ PFPS-LWC & 46.84 & 48 & 48.69 & 40.32 & 39.86 & 40.57 & 33.59 & 34.1 & 33.72 \\ \(\Delta\) & **3.66** & **4.03** & **3.77** & **2.75** & **2.31** & **3.86** & **2.36** & **3.05** & **2.4** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Prediction accuracy of the proposed method compared with that of state-of-the-art methods on Cifar100 using different Dirichlet settings. substantial improvements highlight the effectiveness of our approach in handling highly heterogeneous data distributions and low client participation rates. This further underscores the potential of PFPS-LWC as a robust solution for federated learning in extremely heterogeneous environments. The ability of our method to maintain high accuracy under such challenging conditions demonstrates its versatility and robustness. In addition, we present the accuracy curves of different methods during the training process in Figures 5 and 6. These figures provide a direct comparison of the convergence behavior and stability of our method versus those of others across different heterogeneous environments. As shown in both figures, our method achieved faster convergence compared to that of the other methods, highlighting its efficiency in reaching optimal performance. This is particularly evident in the rapid rise in accuracy in the early stages of training, which suggests that our model is able to quickly adapt to local data distributions. Moreover, both figures consistently demonstrate smaller fluctuations in the accuracy curves for our method. This stability across both figures is a key feature indicating that our model maintains consistent performance throughout the training process, avoiding common issues such as overfitting or underfitting. The reduced fluctuations across both figures can be interpreted as a result of incorporating more local knowledge into the model, which helps it better adapt to the specific characteristics of each client's data. This dual advantage, faster convergence and improved stability, further reinforces the effectiveness and robustness of our approach, making it well suited to handle the challenges posed by data heterogeneity in federated learning environments. Figure 5: The accuracy curves for cifar10 and cifar100 under different Dirichlet partitioning settings.