  This paper considers decentralized stochastic optimization over a network
of~$n$ nodes, where each node possesses a smooth non-convex local cost function
and the goal of the networked nodes is to find an~$\epsilon$-accurate
first-order stationary point of the sum of the local costs. We focus on an
online setting, where each node accesses its local cost only by means of a
stochastic first-order oracle that returns a noisy version of the exact
gradient. In this context, we propose a novel single-loop decentralized hybrid
variance-reduced stochastic gradient method, called \texttt{GT-HSGD}, that
outperforms the existing approaches in terms of both the oracle complexity and
practical implementation. The \texttt{GT-HSGD} algorithm implements specialized
local hybrid stochastic gradient estimators that are fused over the network to
track the global gradient. Remarkably, \texttt{GT-HSGD} achieves a
network-independent oracle complexity of~$O(n^{-1}\epsilon^{-3})$ when the
required error tolerance~$\epsilon$ is small enough, leading to a linear
speedup with respect to the centralized optimal online variance-reduced
approaches that operate on a single node. Numerical experiments are provided to
illustrate our main technical results.
