  We consider the stochastic nested composition optimization problem where the
objective is a composition of two expected-value functions. We proposed the
stochastic ADMM to solve this complicated objective. In order to find an
$\epsilon$ stationary point where the expected norm of the subgradient of
corresponding augmented Lagrangian is smaller than $\epsilon$, the total sample
complexity of our method is $\mathcal{O}(\epsilon^{-3})$ for the online case
and $\mathcal{O} \Bigl((2N_1 + N_2) + (2N_1 + N_2)^{1/2}\epsilon^{-2}\Bigr)$
for the finite sum case. The computational complexity is consistent with
proximal version proposed in \cite{zhang2019multi}, but our algorithm can solve
more general problem when the proximal mapping of the penalty is not easy to
compute.
