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 ...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.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12001430,11972292 and 12161053)the China Postdoctoral Science Foundation(No.2020M683545)the Guangdong Basic and Applied Basic Research Foundation(No.2023A1515012405).
文摘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.
基金国家自然科学基金(the National Natural Science Foundation of China under Grant No.60773062,No.60673045)教育部科学技术研究重点项目(the Key Scientific and Technical Research Project of Ministry of Education of China under Grant No.206012)河北省教育厅科研计划重点项目(the Key Scientific Research Project of Department of Hebei of Education of China under Grant No.2005001D)
基金国家自然科学基金( the National Natural Science Foundation of China under Grant No.60773062) 教育部科学技术研究重点项目( the Key Scientific and Technical Research Project of Ministry of Education of China under Grant No.206012) +1 种基金河北省教育厅科研计划重点项目( the Key Scientific Research Project of Department of Hebei Education of China under Grant No.2005001D) 河北省自然科学基金资助项目( the Natural Science Foundation of Hebei Province of China under Grant No.2008000633)
