  We present a novel method for graph partitioning, based on reinforcement
learning and graph convolutional neural networks. Our approach is to
recursively partition coarser representations of a given graph. The neural
network is implemented using SAGE graph convolution layers, and trained using
an advantage actor critic (A2C) agent. We present two variants, one for finding
an edge separator that minimizes the normalized cut or quotient cut, and one
that finds a small vertex separator. The vertex separators are then used to
construct a nested dissection ordering to permute a sparse matrix so that its
triangular factorization will incur less fill-in. The partitioning quality is
compared with partitions obtained using METIS and SCOTCH, and the nested
dissection ordering is evaluated in the sparse solver SuperLU. Our results show
that the proposed method achieves similar partitioning quality as METIS and
SCOTCH. Furthermore, the method generalizes across different classes of graphs,
and works well on a variety of graphs from the SuiteSparse sparse matrix
collection.
