  This work considers the decentralized successive convex approximation (SCA)
method for minimizing stochastic non-convex objectives subject to convex
constraints, along with possibly non-smooth convex regularizers. Although SCA
has been widely applied in decentralized settings, its stochastic first order
(SFO) complexity is unknown, and it is thought to be slower than the
centralized momentum-enhanced SCA variants. In this work, we advance the
state-of-the-art for SCA methods by proposing an accelerated variant, namely
the \textbf{D}ecentralized \textbf{M}omentum-based \textbf{S}tochastic
\textbf{SCA} (\textbf{D-MSSCA}) and analyze its SFO complexity. The proposed
algorithm entails creating a stochastic surrogate of the objective at every
iteration, which is minimized at each node separately. Remarkably, the D-MSSCA
achieves an SFO complexity of $\mathcal{O}(\epsilon^{-3/2})$ to reach an
$\epsilon$-stationary point, which is at par with the SFO complexity lower
bound for unconstrained stochastic non-convex optimization in centralized
setting.
