  Graph Neural Networks (GNNs) have been widely studied in various graph data
mining tasks. Most existingGNNs embed graph data into Euclidean space and thus
are less effective to capture the ubiquitous hierarchical structures in
real-world networks. Hyperbolic Graph Neural Networks(HGNNs) extend GNNs to
hyperbolic space and thus are more effective to capture the hierarchical
structures of graphs in node representation learning. In hyperbolic geometry,
the graph hierarchical structure can be reflected by the curvatures of the
hyperbolic space, and different curvatures can model different hierarchical
structures of a graph. However, most existing HGNNs manually set the curvature
to a fixed value for simplicity, which achieves a suboptimal performance of
graph learning due to the complex and diverse hierarchical structures of the
graphs. To resolve this problem, we propose an Adaptive Curvature Exploration
Hyperbolic Graph NeuralNetwork named ACE-HGNN to adaptively learn the optimal
curvature according to the input graph and downstream tasks. Specifically,
ACE-HGNN exploits a multi-agent reinforcement learning framework and contains
two agents, ACE-Agent andHGNN-Agent for learning the curvature and node
representations, respectively. The two agents are updated by a NashQ-leaning
algorithm collaboratively, seeking the optimal hyperbolic space indexed by the
curvature. Extensive experiments on multiple real-world graph datasets
demonstrate a significant and consistent performance improvement in model
quality with competitive performance and good generalization ability.
