# A DQN-Based Multi-Objective Participant Selection for Efficient Federated Learning
## 5 Simulation Analysis
### Analysis of Results  
The experiments evaluate four algorithms, including accuracy, loss function, and time delay. In the experiment, the accuracy of the MNIST dataset is calculated as the ratio of correctly classified samples to the total number of samples, considering it is a classification problem. This metric allows for a comprehensive comparison of the performance of the algorithms. We divide the experiment into three groups to present the comparison of accuracy, loss function, and delay under different conditions. Figure 3 presents the accuracy of four algorithms under different conditions of changing the number of iterations, the number of nodes, and the proportion of malicious nodes. Figure 3a illustrates the accuracy variation of the four algorithms when 20% of the nodes are malicious. From Figure 3a, it is evident that the accuracy of the models obtained through the four mechanisms is low during the early stages of training, suggesting that sufficient training iterations are necessary to ensure model accuracy. Upon reaching eight iterations, the accuracy of the models trained by FL-DQN, FL-Random, and FL-Greedy mechanisms tends to stabilize. When the number of iterations reaches 25, the accuracies of FL-DQN, FL-Random, FL-Greedy, and Local Training stabilize around 0.98, 0.96, 0.96, and 0.95, respectively. The FL-DQN algorithm maintains strong training performance when faced with a limited number of malicious nodes and varying data quality. Figure 3b displays the accuracy variation of the four algorithms when 40% of the device nodes are malicious. As observed in Figure 3b, FL-DQN rapidly converges to the highest accuracy (0.98) when confronted with a large number of malicious nodes. In contrast, the model quality obtained by FL-Random decreases due to the influence of malicious nodes and stabilizes around 0.95, which is comparable to the training performance of Local Training. For the FL-Greedy algorithm, the accuracy decreases to 0.93. The FL mechanism proposed in this study successfully balances data quality and device training, effectively ensuring optimal model quality. Figure 3: Accuracy experimental group. Figure 3c presents the model accuracy achieved by the four algorithms for different numbers of nodes. The FL-DQN algorithm achieves the highest accuracy when dealing with various node quantities. For example, when 40 nodes are considered, the accuracy of the four algorithms is 0.967, 0.938, 0.932, and 0.754, respectively. The accuracy of FL-DQN algorithm improves by 3.0% and 22.0% compared to FL-DQN and Local Training, respectively. The results also demonstrate that the proposed method exhibits strong scalability in terms of node size, maintaining peak performance as the number of nodes increases. Figure 3d presents the accuracy of the models obtained by the four algorithms for a fixed number of training rounds (30 rounds) and different percentages of malicious nodes (ranging from 10% to 80%). We observe that FL-DQN can efficiently filter out high-quality nodes for model aggregation when dealing with different proportions of malicious nodes, in contrast to FL-Random, FL-Greedy and Local Training. This filtering process ensures the quality of the overall model, leading to the highest accuracy and smallest loss function values in FL-DQN. As a result, it can be concluded that the proposed method exhibits excellent robustness. Figure 4 presents the loss functions of four algorithms under different conditions of changing the number of iterations, the number of nodes, and the proportion of malicious nodes. Figure 4a presents the variation of the loss functions for the four algorithms when 20% of the nodes are malicious. The FL-DQN algorithm converges faster than the remaining four algorithms and exhibits the lowest value for the loss function. This also highlights the advantages of the FL-DQN approach in terms of convergence and loss reduction. Figure 4b shows the variation of the loss functions of the four algorithms when 40% of the malicious nodes are present.