  It is well established that graph neural networks (GNNs) can be interpreted
and designed from the perspective of optimization objective. With this clear
optimization objective, the deduced GNNs architecture has sound theoretical
foundation, which is able to flexibly remedy the weakness of GNNs. However,
this optimization objective is only proved for GNNs with single-relational
graph. Can we infer a new type of GNNs for multi-relational graphs by extending
this optimization objective, so as to simultaneously solve the issues in
previous multi-relational GNNs, e.g., over-parameterization? In this paper, we
propose a novel ensemble multi-relational GNNs by designing an ensemble
multi-relational (EMR) optimization objective. This EMR optimization objective
is able to derive an iterative updating rule, which can be formalized as an
ensemble message passing (EnMP) layer with multi-relations. We further analyze
the nice properties of EnMP layer, e.g., the relationship with multi-relational
personalized PageRank. Finally, a new multi-relational GNNs which well
alleviate the over-smoothing and over-parameterization issues are proposed.
Extensive experiments conducted on four benchmark datasets well demonstrate the
effectiveness of the proposed model.
