  In this paper, we develop a symmetric accelerated stochastic Alternating
Direction Method of Multipliers (SAS-ADMM) for solving separable convex
optimization problems with linear constraints. The objective function is the
sum of a possibly nonsmooth convex function and an average function of many
smooth convex functions. Our proposed algorithm combines both ideas of ADMM and
the techniques of accelerated stochastic gradient methods using variance
reduction to solve the smooth subproblem. One main feature of SAS-ADMM {is}
that its dual variable is symmetrically updated after each update of the
separated primal variable, which would allow a more flexible and larger
convergence region of the dual variable compared with that of standard
deterministic or stochastic ADMM. This new stochastic optimization algorithm is
shown to converge in expectation with $\C{O}(1/T)$ convergence rate, where $T$
is the number of outer iterations. In addition, 3-block extensions of the
algorithm and its variant of an accelerated stochastic augmented Lagrangian
method are also discussed. Our preliminary numerical experiments indicate the
proposed algorithm is very effective for solving separable optimization
problems from big-data applications
