# Improving Graph Neural Network Models in Link Prediction Task via A Policy-Based Training Method
## 2 Preliminary
### Graph Neural Network in Link Prediction Task  
Graph neural network (GNN) models are deep learning models operating directly on graph-structured data, which are generalizations of the convolutional neural network in the non-Euclidean domain [19]. Here, we only briefly introduce several typical GNN models. [PERSON] et al. [20] propose the Spectral Graph CNN extending convolutions to general graphs by using the graph Fourier transform. The Spectral Graph CNN is the pioneering work of GNN models. [PERSON] et al. [1] propose the graph convolutional network (GCN), which aggregates information in one-hop neighborhoods of each node. [PERSON] et al. [15] present the GraphSAGE, which obtains the convolved features of nodes by sampling and  
Figure 1: Examples of false and easy negative samples. Edges in (**a–c**) represent the edges in \(E_{train}^{pos}\), \(E_{valid}^{pos}\) and \(E_{test}^{pos}\), respectively. The missing edges, including edge \((v_{3},v_{7})\) in (**d**) and edge \((v_{1},v_{2})\) in (**e**), are sampled as negative samples, which mislead GNN models. The easily distinguishable edge \((v_{1},v_{6})\) in (**f**) is sampled as a negative sample, which contributes insufficiently to GNN models.  
aggregating their neighbors. [PERSON] et al. [16] present the graph attention network (GAT) taking advantage of masked self-attention in the graph convolutional architecture.  
As an important task in graph mining, increasing studies attempt to introduce the aforementioned GNN models into the link prediction tasks. In the study of [PERSON] et al. [7], the authors find that the over-reliance on predefined assumptions about the existence of edges limits the performance of traditional link prediction methods. They propose a link prediction method (SEAL) using GNN to automatically evaluate the existence of edges from the subgraph. [PERSON] et al. [10] propose a framework, named NBFNet, that can be utilized in the link prediction task. The NBFNET framework leverages a GNN model to obtain edge representations from the paths between two nodes. Moreover, this framework is applicable to both homogeneous graphs and knowledge graphs. Inspired by variational auto-encoder (VAE), [PERSON] et al. [5] propose two models, including variational graph auto-encoder (VGAE) and graph auto-encoder (GAE). Due to the ability of GAE to incorporate the feature of nodes, benchmarking GNN models [13] and many studies [6; 8; 9; 11; 12] in the link prediction tasks have adopted the graph auto-encoder (GAE) framework. The methods using the GAE framework generally have two modules, including the encoder and decoder. [PERSON] et al. [6] propose a GC-MC framework, which is an extension of the GAE framework solving the matrix completion in the form of link prediction. In the GC-MC framework, the encoder generates node features through message passing, and the decoder utilizes a bilinear operation to evaluate the existence of edges. The Graphite proposed by [PERSON] et al. [8] also has an encoder and decoder. The authors use GNN models as the encoder and use an iterative approach with two steps to calculate the edge probabilities in a graph. [PERSON] et al. [9] propose a FastGAE framework to accelerate the training process of the GAE framework in real-world graphs. This framework introduces a node sampling approach and constructs the decoder on the subgraph. [PERSON] et al. [11] propose a MSVGAE framework to remove the deficiency of the GAE framework and employ a self-supervised learning method to make sufficient use of the graph attributes. [PERSON] et al. [12] propose a message-passing scheme that takes advantage of both structure and community information in a graph. The message-passing scheme can be used in the encoder of the GAE framework, which is shown to be effective in the link prediction task.