## 4 Experiments
### Results  
Tables 1-6 show the experimental results of the three models. The experimental results are divided into two parts, with Formulas (22) and (26) as the objective function, respectively. The results of each part consist of the following parts:  
* The average value of the average mastery of knowledge points of each student in the class;
* The number of students whose average mastery of knowledge points exceeds 0.6;
* The number of students whose average mastery of knowledge points exceeds 0.8;
* The standard deviation of the average mastery of knowledge points in the class.  
For the EFC model, it can be observed in Table 1 that the DRL method is significantly better than the random and linear methods. DRL is similar to cyclic and threshold methods. When Formula (26) is used as the objective function, DRL has a better effect. At the same time, the standard deviation of DRL-based students' performance is the smallest in all cases. Table 2 shows the results after disassociating the knowledge points. The general situation is the same as in Table 1. The DRL method also performs better when Formula (22) is used as the objective function.  
The effect of the HLR model implemented in Table 3 differs from that of the EFC model. The effect of the linear method was improved. DRL achieved the best results in terms of average grade, pass rate, excellent rate, and standard deviation. When we cancelled the knowledge point association, the result shown in Table 4 was obtained. The effect of linear teaching was greatly improved. The DRL method was second only to the linear method.  
Table 5 shows that the DRL method is superior to other methods in all aspects of the BKT model. When we canceled the knowledge point association, it can be observed in Table 6 that the DRL method did not differ greatly from the other methods. This is because the BKT model does not consider the forgetting strategy, so four methods can obtain a good result.  
After experimenting with a random combination of multiple targets, the result in Table 7 shows that adding each sub-reward to the reward of Formula (22) will improve the effect of DRL, which proves that the reward function we proposed is both reasonable and effective. Through the above experiments, it can be seen that each of the four comparison strategy methods have advantages and disadvantages. In contrast, DRL achieves good  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Method** & **Average** & **Pass** & **Excellent** & **SD** & **Average** (log)** & **Pass (log)** & **Excellent** & **SD (log)** \\ \hline Random & 0.553 & 7 & 0 & 0.096 & 0.528 & 6 & 0 & 0.110 \\ Linear & 0.624 & 12 & 3 & 0.120 & 0.575 & 7 & 1 & 0.121 \\ Cyclic & 0.633 & 13 & 3 & 0.123 & 0.580 & 8 & 1 & 0.126 \\ Threshold & 0.633 & 13 & 3 & 0.124 & 0.583 & 8 & 1 & 0.127 \\ DRL & 0.633 & 12 & 3 & 0.123 & 0.581 & 8 & 1 & 0.126 \\ \hline \hline \end{tabular}
\end{table}
Table 6: The results of BKT that do not consider the knowledge point association.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Average** & **Pass** & **Excellent** \\ \hline
12 & 0.405 & 5 & 3 \\
13 & 0.406 & 6 & 0 \\
23 & 0.429 & 6 & 2 \\ DRL(123) & 0.437 & 6 & 3 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Component comparison experiment.  
results in all cases. In some of the experiments, DRL did not obtain the best teaching results but obtained higher rewards due to the algorithm setting a larger discount factor to quickly improve the performance in the early stage to improve the overall rewards. The effectiveness of DRL does not depend on a specific context, which proves the efficiency and generality of the method. Furthermore, a multi-part randomized combination experiment verified that each part of the reward function setting was beneficial. Thus, DRL, as the group teaching recommendation algorithm used in the system, can meet the system design requirements for this recommendation function.