# Personalized Federated Learning with Progressive Local Training Strategy and Lightweight Classifier
## 4 Experiments
### A Comparison with State-of-the-Art Methods

Table 2: Prediction accuracy of the proposed method compared with that of state-of-the-art methods on Cifar10 using different Dirichlet settings. In Table 4, we present the experimental results for cifar10 and cifar100 under pathological data partitioning. As shown in the table, our method achieved optimal results in this scenario. Specifically, when the dataset was cifar100 with \(p=0.5\), PFPS-LWC surpassed FedPer's accuracy by up to 3.57%. This demonstrates that our method is effective when the data volume is similar but the types of data differ. It also highlights the importance of retaining local knowledge to mitigate the interference from other types of knowledge. A thorough examination of Tables 2-4 reveals a compelling observation: under various environmental settings, PFPS-LWC consistently achieved the best results on both the cifar10 and cifar100 datasets, outperforming other methods. This substantial evidence demonstrates the robustness of PFPS-LWC in highly heterogeneous environments and with varying client participation rates. Under different environmental settings, PFPS-LWC also significantly outperformed the baseline, further validating its versatility and robustness. This remarkable advantage underscores the necessity of PFPS-LWC's improvements to the original pFL framework. It supports our viewpoint that simply using the global model to initialize local models is unreasonable. Instead, our approach, which focuses on improving the continuity of local training and alleviating local knowledge forgetting, proves to be more effective. By ensuring that local models retain valuable knowledge from previous training rounds and seamlessly integrate global information, PFPS-LWC enhances the overall effectiveness of federated model training. Additionally, compared to traditional federated learning methods like FedAvg [29] and FedProx [14], our method significantly outperformed them. In extreme heterogeneous conditions with \(\beta=0.1\) and \(P=0.3\), as shown in Table 3, our method exceeded their accuracy on the cifar10 dataset by an impressive 57.55% and 54.23%, respectively. These \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{4}{c}{**Accuracy\(\dagger\) Predicted with Different Pathological Settings**} \\ \cline{2-7}  & \multicolumn{2}{c}{**Cifar10**} & \multicolumn{4}{c}{**Cifar100**} \\ \cline{2-7}  & \(P=0.3\) & \(P=0.5\) & \(P=0.7\) & \(P=0.3\) & \(P=0.5\) & \(P=0.7\) \\ \hline FedAvg [29] & 44.78 & 59.55 & 60.99 & 20.35 & 22.64 & 25.12 \\ FedProx [14] & 49.28 & 60.48 & 62.76 & 20.68 & 23.94 & 26.01 \\ FedPer [20] & 74.68 & 74.68 & 74.66 & 39.12 & 40.13 & 40.32 \\ pFedMe [37] & 65.17 & 65.9 & 66.78 & 24.68 & 26.43 & 25.38 \\ FedBN [23] & 65.16 & 70.5 & 71.75 & 26.6 & 29.56 & 31.88 \\ FedProto [41] & 71.05 & 70.74 & 71.01 & 37.19 & 34.31 & 36.86 \\ PFPS-LWC & 76.06 & 76.29 & 76.64 & 41.9 & 43.7 & 43.35 \\ \(\Delta\) & **1.38** & **1.61** & **2.22** & **2.78** & **3.57** & **3.03** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Prediction accuracy of the proposed method compared with that of state-of-the-art methods on Cifar10 and Cifar100 using different pathological settings.