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We present a novel method for graph partitioning, based on reinforcementlearning and graph convolutional neural networks. Our approach is torecursively partition coarser representations of a given graph. The neuralnetwork is implemented using SAGE graph convolution layers, and trained usingan advantage actor critic (A2C) agent. We present two variants, one for findingan edge separator that minimizes the normalized cut or quotient cut, and onethat finds a small vertex separator. The vertex separators are then used toconstruct a nested dissection ordering to permute a sparse matrix so that itstriangular factorization will incur less fill-in. The partitioning quality iscompared with partitions obtained using METIS and SCOTCH, and the nesteddissection ordering is evaluated in the sparse solver SuperLU. Our results showthat the proposed method achieves similar partitioning quality as METIS andSCOTCH. Furthermore, the method generalizes across different classes of graphs,and works well on a variety of graphs from the SuiteSparse sparse matrixcollection.

Graph Partitioning and Sparse Matrix Ordering using Reinforcement Learning and Graph Neural Networks