# Personalized Federated Learning with Progressive Local Training Strategy and Lightweight Classifier
## 4 Experiments
### Ablation Experiments  
To validate the effectiveness of Module 3.2 (the Progressive Local Training Strategy) and Module 3.3 (the lightweight classifier), we conducted a series of ablation experiments. These experiments were performed on the cifar10 dataset with \(\beta=0.5\) and \(P=[0.3,0.5,0.7]\), as well as on the cifar100 dataset with \(\beta=0.5\) and \(P=[0.3,0.5,0.7]\). By varying these parameters, we aimed to simulate different levels of data heterogeneity and client participation rates, providing a comprehensive evaluation of our proposed modules.  
The results of these ablation experiments are presented in Table 5 below. This table illustrates the overall effectiveness of the different modules, highlighting the contributions of each component to the performance of our method. By isolating the impact of the Progressive Local Training Strategy and the lightweight classifier, we could better understand their individual and combined effects on the model accuracy and stability.  
From the table, we can observe that both modules improved the algorithm's performance to varying degrees. For instance, on the cifar10 dataset, the Progressive Local Training (PLT) module, with \(\beta=5\) and \(P=0.3\), showed a 3.53% improvement over the baseline. This improvement highlights the effectiveness of the PLT module in enhancing  
Figure 6: The accuracy curves for cifar10 and cifar100 under different pathological partitioning settings.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Module**} & \multicolumn{3}{c}{**Cifar10 (\(\beta=0.5\))**} & \multicolumn{3}{c}{**Cifar100 (\(\beta=0.1\))**} \\ \hline
**PLT** & **LWC** & \(P=0.3\) & \(P=0.5\) & \(P=0.7\) & \(P=0.3\) & \(P=0.5\) & \(P=0.7\) \\ \hline \(\times\) & \(\times\) & 75.59 & 76.21 & 76.4 & 43.18 & 43.97 & 44.92 \\ \(\checkmark\) & \(\times\) & 79.13 (3.54) & 79.32 (3.11) & 78.9 (2.52) & 45.87 (2.69) & 45.9 (1.93) & 46.64 (1.72) \\ \(\times\) & \(\checkmark\) & 76.87 (1.28) & 77.15 (0.94) & 78.26 (1.86) & 44.31 (1.13) & 46.12 (2.15) & 46.95 (2.03) \\ \(\checkmark\) & \(\checkmark\) & 79.77 (4.18) & 80.43 (4.22) & 80.33 (3.93) & 46.84 (3.66) & 48 (4.03) & 48.69 (3.77) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Ablation study: \(\checkmark\) indicates module usage, \(\times\) indicates module non-usage.  
the model's ability to retain and utilize local knowledge, thereby improving its performance in heterogeneous environments. On the cifar100 dataset, the lightweight classifier (LWC) module, with \(\beta=0.1\) and \(P=0.5\), demonstrated a 2.15% improvement over the baseline. This result underscores the importance of regularizing the classifier head, which undergoes prolonged local training. By incorporating an LWC, the classifier's generalization capability is enhanced, leading to better overall performance.  
These experiments demonstrate that both modules significantly enhance the performance of our method, particularly in environments with high data heterogeneity and varying client participation rates. The Progressive Local Training Strategy helps to maintain continuity in local training, while the LWC improves the generalization capability of the classifier. Together, these modules contribute to a more robust and effective federated learning framework.