Abstract
Graphs can be used to represent and reason about systems and a variety of metrics have been devised to quantify their global characteristics. However, little is currently known about how to construct a graph or improve an existing one given a target objective. In this work, we formulate the construction of a graph as a decision-making process in which a central agent creates topologies by trial and error and receives rewards proportional to the value of the target objective. By means of this conceptual framework, we propose an algorithm based on reinforcement learning and graph neural networks to learn graph construction and improvement strategies. Our core case study focuses on robustness to failures and attacks, a property relevant for the infrastructure and communication networks that power modern society. Experiments on synthetic and real-world graphs show that this approach can outperform existing methods while being cheaper to evaluate. It also allows generalization to out-of-sample graphs, as well as to larger out-of-distribution graphs in some cases. The approach is applicable to the optimization of other global structural properties of graphs.
Highlights
Graphs are mathematical abstractions that can be used to model a variety of systems, from infrastructure and biological networks to social structures
Combining Graph Neural Network (GNN) with RL algorithms has yielded models capable of solving several graph optimisation problems with the same architecture while generalising to graphs an order of magnitude larger than those used during training [32]
We have addressed the problem of improving a graph structure given the goal of maximising the value of a global objective function
Summary
Graphs are mathematical abstractions that can be used to model a variety of systems, from infrastructure and biological networks to social structures. 3 edge additions over a sequence of 6 node selections (actions At ), receiving rewards Rt proportional to the value of an objective function F applied to the graph In this case, F quantifies the robustness of the network to targeted node removal, computed by removing nodes in decreasing order of their degree and in decreasing order of the labels if two nodes have the same degree. With the goal of discovering better strategies than existing methods, we ask whether generalisable network construction strategies for improving robustness can be learned Starting from this motivation, we formalise the process of graph construction and improvement as a Markov Decision Process (MDP) in which rewards are proportional to the value of a graph-level objective function.
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