  Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an
indispensable strategy to speed up training large-scale Graph Neural Networks
(GNNs). However, existing sampling methods are mostly based on the graph
structural information and ignore the dynamicity of optimization, which leads
to high variance in estimating the stochastic gradients. The high variance
issue can be very pronounced in extremely large graphs, where it results in
slow convergence and poor generalization. In this paper, we theoretically
analyze the variance of sampling methods and show that, due to the composite
structure of empirical risk, the variance of any sampling method can be
decomposed into \textit{embedding approximation variance} in the forward stage
and \textit{stochastic gradient variance} in the backward stage that
necessities mitigating both types of variance to obtain faster convergence
rate. We propose a decoupled variance reduction strategy that employs
(approximate) gradient information to adaptively sample nodes with minimal
variance, and explicitly reduces the variance introduced by embedding
approximation. We show theoretically and empirically that the proposed method,
even with smaller mini-batch sizes, enjoys a faster convergence rate and
entails a better generalization compared to the existing methods.
