1,064 research outputs found
A first-order stochastic primal-dual algorithm with correction step
We investigate the convergence properties of a stochastic primal-dual
splitting algorithm for solving structured monotone inclusions involving the
sum of a cocoercive operator and a composite monotone operator. The proposed
method is the stochastic extension to monotone inclusions of a proximal method
studied in {\em Y. Drori, S. Sabach, and M. Teboulle, A simple algorithm for a
class of nonsmooth convex-concave saddle-point problems, 2015} and {\em I.
Loris and C. Verhoeven, On a generalization of the iterative soft-thresholding
algorithm for the case of non-separable penalty, 2011} for saddle point
problems. It consists in a forward step determined by the stochastic evaluation
of the cocoercive operator, a backward step in the dual variables involving the
resolvent of the monotone operator, and an additional forward step using the
stochastic evaluation of the cocoercive introduced in the first step. We prove
weak almost sure convergence of the iterates by showing that the primal-dual
sequence generated by the method is stochastic quasi Fej\'er-monotone with
respect to the set of zeros of the considered primal and dual inclusions.
Additional results on ergodic convergence in expectation are considered for the
special case of saddle point models
Scalable Peaceman-Rachford Splitting Method with Proximal Terms
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 convergence rate, which is the same as those
newest stochastic algorithms that based on ADMM but faster than general
Stochastic ADMM (which is ). 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
- …