GraphRARE: Reinforcement Learning Enhanced Graph Neural Network with Relative Entropy

TL;DR

GraphRARE tackles the challenge of heterophilic graphs by introducing a node-relative-entropy framework that fuses node features and local structure, enabling meaningful cross-node connections. A deep reinforcement learning module then adaptively selects per-node topology changes (top-k additions and top-d deletions) to optimize GNN performance in an end-to-end loop. The approach yields consistent improvements across heterophilic datasets and maintains competitiveness on homophilic graphs, with ablation studies confirming the importance of both the entropy metric and the DRL-driven topology optimization. Overall, GraphRARE broadens GNN applicability to diverse graphs by jointly learning topology and representation, offering a scalable, end-to-end method with practical efficiency gains. Potential extensions include multi-modal and spatial-temporal graphs.

Abstract

Graph neural networks (GNNs) have shown advantages in graph-based analysis tasks. However, most existing methods have the homogeneity assumption and show poor performance on heterophilic graphs, where the linked nodes have dissimilar features and different class labels, and the semantically related nodes might be multi-hop away. To address this limitation, this paper presents GraphRARE, a general framework built upon node relative entropy and deep reinforcement learning, to strengthen the expressive capability of GNNs. An innovative node relative entropy, which considers node features and structural similarity, is used to measure mutual information between node pairs. In addition, to avoid the sub-optimal solutions caused by mixing useful information and noises of remote nodes, a deep reinforcement learning-based algorithm is developed to optimize the graph topology. This algorithm selects informative nodes and discards noisy nodes based on the defined node relative entropy. Extensive experiments are conducted on seven real-world datasets. The experimental results demonstrate the superiority of GraphRARE in node classification and its capability to optimize the original graph topology.

Figures (8)

• Figure 1: The visual illustration of related works on heterophilic graph neural networks. The color shades indicate the effectiveness of node selection in reconstructing the original graph topology, with darker shades representing higher effectiveness.
• Figure 2: An illustration of the proposed GraphRARE framework. The GNN and DRL module are trained jointly to optimize the graph topology based on the relative entropy (the depth of the node's color indicates the value of entropy).
• Figure 3: The agent environment interaction in RL.
• Figure 4: An illustration of the graph topology optimization module. For any node $v$ in the graph $G_t$ at step $t$, the graph optimization module generates graph $G_{t+1}$ via adding $k_v$ edges and removing $d_v$ edges for node $A$ based on the state $S_t$. For node $A$ in this example, $k_A=3$ edges are added and $d_A=2$ edges are removed.
• Figure 5: Ablation study on the DRL module's contribution. Each heatmap compares GraphRARE's performance with and without the DRL module. The horizontal axis represents the number of deleted edges ($d$), while the vertical axis represents the number of added edges ($k$). Deeper colors indicate more significant performance degradation compared to GraphRARE.

Theorems & Definitions (1)

• Definition 1: Topology Optimization for GNNs