Neural Maximum Independent Set

The emergence of deep learning brought solutions to many difficult problems and has recently motivated new studies that try to solve hard combinatorial optimization problems with machine learning approaches. We propose a framework based on Expert Iteration, an imitation learning method that we apply to solve combinatorial optimization problems on graphs, in particular the Maximum Independent Set problem. Our method relies on training GNNs to recognize how to complete a solution, given a partial solution of the problem as an input. This paper emphasizes some interesting findings such as the introduction of learned nodes features helping the neural network to give relevant solutions. Moreover, we represent the space of good solutions and discuss the ability of GNN's to solve the problem on a graph without training on it.