Accelerated Stochastic Peaceman–Rachford Method for Empirical Risk Minimization

This work is devoted to studying an accelerated stochastic Peaceman–Rachford splitting method (AS-PRSM) for solving a family of structural empirical risk minimization problems. The objective function to be optimized is the sum of a possibly nonsmooth convex function and a finite sum of smooth convex component functions. The smooth subproblem in AS-PRSM is solved by a stochastic gradient method using variance reduction technique and accelerated techniques, while the possibly nonsmooth subproblem is solved by introducing an indefinite proximal term to transform its solution into a proximity operator. By a proper choice for the involved parameters, we show that AS-PRSM converges in a sublinear convergence rate measured by the function value residual and constraint violation in the sense of expectation and ergodic. Preliminary experiments on testing the popular graph-guided fused lasso problem in machine learning and the 3D CT reconstruction problem in medical image processing show that the proposed AS-PRSM is very efficient.