## 4 Proposed Method
### Overview of Method  
In this part, we provide a formal description of the encoder, which generates embeddings for all input nodes. We then present two decoders, which consist of a Pseudo-label generation decoder and a sequential outcome decoder. At each iteration, Algorithm 1 should perform the following procedures, as shown in Figure 2. As described above, the neural network model utilized in this pa, er, which is shown in Figure 3, consists of an encoder and two decoders.  
First, parameters are input, comprising the total number of training epochs \(E\), the number of steps per epoch \(T\), the batch size \(B\), and the significance level \(\sigma\). Then, parameters are initialized, including initializing the current policy parameters \(\theta\) and a reference policy parameter \(\theta^{*}\). Second, iterate over each step in each epoch. Third, sample actions \(\pi_{i}\) from the current policy \(P_{\theta}\) and \(\pi_{i}^{*}\) from the GreedyBaseline policy, for instance, \(s^{*}\), then compute the total loss function \(L_{\theta}\), which includes policy loss \(L_{s}(\theta)\) and policy gradient loss \(L_{p}(\theta)\), and update the policy parameters \(\theta\) using the Adam optimizer to minimize the loss function. Finally, determine whether to stop by comparing whether the performance difference between the current policy \(P_{\theta}\) and the reference policy \(P_{\theta^{*}}\) is significant.  
Figure 3: The overall architecture of our PGDD model, which illustrates the encoder, two decoders, and their corresponding inputs and outputs.  
Figure 2: Flowchart of the PGDD method.  
```
0: Training dataset \(\mathcal{D}\) with \(N\) nodes per instance  Number of epochs \(E\), batch size \(B\), learning rate \(\eta\)  Exploration rate \(\epsilon\), pseudo-label confidence threshold \(\tau=0.8\)
```
0: Trained PGDD model parameters \(\theta\) Initialize:  Encoder parameters \(\theta_{\text{enc}}\), decoder parameters \(\theta_{\text{dec1}},\theta_{\text{dec2}}\)  Reference policy parameters \(\theta^{*}\leftarrow\theta_{\text{dec1}}\) for\(\text{epoch}=1\) to \(E\)do for\(\text{batch}=1\) to \(\lceil\left|\mathcal{D}\right|/B\rceil\)do  Sample batch \(\mathcal{B}\) from \(\mathcal{D}\)  Encoder:  Generate node embeddings \(h_{i}=\text{Encoder}(x_{i};\theta_{\text{enc}})\)  Compute graph embedding \(h_{g}=\frac{1}{N}\sum_{i=1}^{N}h_{i}\) Decoder 1 (Pseudo-Label Generation):  Use RL to sample path \(\pi\sim P_{\theta_{\text{dec1}}}(\pi|h_{i},h_{g})\)  Compute policy loss \(\mathcal{L}_{p}=\mathbb{E}_{\pi}[\mathbb{C}(\pi)]-b(\mathcal{B})\) Decoder 2 (Sequential Outcome):  Predict edge probabilities \(S=\text{Decoder2}(h_{i},h_{g};\theta_{\text{dec2}})\)  Generate pseudo-labels \(\hat{S}=\mathbb{I}(\pi)\) \(\triangleright\) Convert path \(\pi\) to adjacency matrix  Compute cross-entropy loss \(\mathcal{L}_{s}=\text{CE}(S,\hat{S})\) Update Parameters:  Total loss \(\mathcal{L}=\mathcal{L}_{p}+\lambda\mathcal{L}_{s}\) (\(\lambda=1\))  Update \(\theta\leftarrow\text{Adam}(\theta,\
abla_{\theta}\mathcal{L},\eta)\) if\(\text{Performance}(\theta_{\text{dec1}})>\text{Performance}(\theta^{*})+\epsilon\)then  Update reference policy \(\theta^{*}\leftarrow\theta_{\text{dec1}}\) endif endfor endfor ```  
**Algorithm 1** PGDD Training Algorithm