# Personalized Federated Learning with Progressive Local Training Strategy and Lightweight Classifier
## 4 Experiments  
### Experiment Setup  
**Datasets.** To evaluate the effectiveness of the proposed federated learning method, we conducted comprehensive experiments on two widely adopted and challenging visual benchmark datasets:  
* Cifar10 [47]: The CIFAR10 dataset contains 60,000 32 \(\times\) 32 color images, evenly distributed across 10 different classes, with each class comprising 6000 images. Among them, 5000 were used for training and 1000 for testing.  
* Cifar100 [47]: An extension of CIFAR10, the CIFAR100 dataset includes 60,000 32 \(\times\) 32 color images, evenly distributed across 100 classes, with each class containing 600 images. Among them, 500 were used for training and 100 for testing.  
For each dataset, we employed two data partitioning methods. The first method used the Dirichlet distribution to partition the data, which were then allocated to each client. In Dirichlet partitioning, the parameter controlling the Dirichlet distribution, denoted as \(\beta\), can be adjusted to control the degree of Non-IID data among different clients. A smaller \(\beta\) indicated a higher degree of Non-IID data, allowing us to simulate varying levels of heterogeneity by adjusting the value of \(\beta\). The second method was pathological Non-IID partitioning, a manually designed Non-IID data partitioning method. This method 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. We conducted experiments under these two heterogeneity simulation settings. This extensive experimental setup simulated real-world scenarios and ensured a comprehensive evaluation of the robustness of our method. In order to more intuitively understand the two partitioning methods, we present a figure showing two data distributions created using Dirichlet partitioning and pathological Non-IID partitioning on the cifar10 dataset below, where the number of clients, N, was 10 and the Dirichlet distribution parameter \(\beta\) = 0.5. The specific distribution after partitioning is shown in Figure 4 below.  
**Models.** For classification tasks on the above datasets, we used a five-layer CNN network. The first four layers of the CNN served as feature extractors, while the final layer functioned as the classifier. For the CIFAR10 dataset, the output dimension of the final layer was set to 10, while for the CIFAR100 task, the output dimension of the final layer was set to 100.  
**Counterparts.** To demonstrate the effectiveness of the proposed method, we select a representative and superior personalized federated learning method including FedPer [20], FedBN [23], pFedMe [37] and FedProto [41]. Additionally, to showcase the superiority of personalized federated learning on Non-IID data, we also compared our method with the representative of traditional personalized federated learning methods such as FedAvg [29] and FedProx [14].  
**Implementation details.** To ensure the fairness of the comparison methods, we used the same hyperparameters in our experiments. In the experiments, we set the number of clients, \(N\), to 10, the number of global training rounds, \(T\), to 20, and the number of local training epochs, \(E\), to 5. We used an SGD optimizer with a learning rate of 0.01 and a  
Figure 4: The distribution of the cifar10 dataset under two data partitioning methods. (**a**) shows the data distribution after applying Dirichlet partitioning on cifar10 when \(N=10\) and \(\beta=0.5\), while (**b**) illustrates the data distribution after applying Pathological Non-IID partitioning on cifar10 when \(N=10\).  
batch size of 64. Additionally, we set the parameter \(\lambda\) in the PFPS-LWC method to 0.02. The top-one accuracy was used for the evaluation.