Learning Combinatorial Optimization Algorithms over Graphs

Many combinatorial optimization problems over graphs are NP-hard, and require significant specialized knowledge and trial-and-error to design good heuristics or approximation algorithms. Can we automate this challenging and tedious process, and learn the algorithms instead? In many real world applications, it is typically the case that the same type of optimization problem is solved again and again on a regular basis, maintaining the same problem structure but differing in the data. This provides an opportunity for learning heuristic algorithms which can exploit the structure of such recurring problems. In this paper, we propose a unique combination of reinforcement learning and graph embedding to address this challenge. The learned greedy policy behaves like a meta-algorithm which incrementally constructs a solution, and the action is determined by the output of a graph embedding network capturing the current state of the solution. We show that our framework can be applied to a diverse range of optimization problems over graphs, and provide evidence that our learning approach can compete with or outperform specialized heuristics or approximation algorithms for the Minimum Vertex Cover, Maximum Cut and Traveling Salesman Problems.