  Along with developing of Peaceman-Rachford Splittling Method (PRSM), many
batch algorithms based on it have been studied very deeply. But almost no
algorithm focused on the performance of stochastic version of PRSM. In this
paper, we propose a new stochastic algorithm based on PRSM, prove its
convergence rate in ergodic sense, and test its performance on both artificial
and real data. We show that our proposed algorithm, Stochastic Scalable PRSM
(SS-PRSM), enjoys the $O(1/K)$ convergence rate, which is the same as those
newest stochastic algorithms that based on ADMM but faster than general
Stochastic ADMM (which is $O(1/\sqrt{K})$). Our algorithm also owns wide
flexibility, outperforms many state-of-the-art stochastic algorithms coming
from ADMM, and has low memory cost in large-scale splitting optimization
problems.
