  With the large rising of complex data, the nonconvex models such as nonconvex
loss function and nonconvex regularizer are widely used in machine learning and
pattern recognition. In this paper, we propose a class of mini-batch stochastic
ADMMs (alternating direction method of multipliers) for solving large-scale
nonconvex nonsmooth problems. We prove that, given an appropriate mini-batch
size, the mini-batch stochastic ADMM without variance reduction (VR) technique
is convergent and reaches a convergence rate of $O(1/T)$ to obtain a stationary
point of the nonconvex optimization, where $T$ denotes the number of
iterations. Moreover, we extend the mini-batch stochastic gradient method to
both the nonconvex SVRG-ADMM and SAGA-ADMM proposed in our initial manuscript
\cite{huang2016stochastic}, and prove these mini-batch stochastic ADMMs also
reaches the convergence rate of $O(1/T)$ without condition on the mini-batch
size. In particular, we provide a specific parameter selection for step size
$\eta$ of stochastic gradients and penalty parameter $\rho$ of augmented
Lagrangian function. Finally, extensive experimental results on both simulated
and real-world data demonstrate the effectiveness of the proposed algorithms.

Optimization and Control;Machine Learning;Machine Learning