-

 

 

 




Optimization Online





 

Stochastic Variance-Reduced Prox-Linear Algorithms for Nonconvex Composite Optimization

Junyu Zhang(zhan4393***at***umn.edu)
Lin Xiao(lin.xiao***at***microsoft.com)

Abstract: We consider minimization of composite functions of the form $f(g(x))+h(x)$, where $f$ and $h$ are convex functions (which can be nonsmooth) and $g$ is a smooth vector mapping. In addition, we assume that $g$ is the average of finite number of component mappings or the expectation over a family of random component mappings. We propose a class of stochastic variance-reduced prox-linear algorithms for solving such problems and bound their sample complexities for finding an $\epsilon$-stationary point in terms of the total number of evaluations of the component mappings and their Jacobians. When $g$ is a finite average of $N$ components, we obtain sample complexity $O(N+ N^{4/5}\epsilon^{-1})$ for both mapping and Jacobian evaluations. When $g$ is a general expectation, we obtain sample complexities of $O(\epsilon^{-5/2})$ and $O(\epsilon^{-3/2})$ for component mappings and their Jacobians respectively. If in addition $f$ is smooth, then improved sample complexities of $O(N+N^{1/2}\epsilon^{-1})$ and $O(\epsilon^{-3/2})$ are derived for $g$ being a finite average and a general expectation respectively, for both component mapping and Jacobian evaluations.

Keywords: stochastic composite optimization, nonsmooth optimization, variance reduction, prox-linear algorithm, sample complexity

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Nonlinear Optimization

Category 3: Stochastic Programming

Citation: Microsoft Research Technical Report: MSR-TR-2020-11

Download: [PDF]

Entry Submitted: 04/08/2020
Entry Accepted: 04/08/2020
Entry Last Modified: 04/08/2020

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society