- Stochastic Variance-Reduced Prox-Linear Algorithms for Nonconvex Composite Optimization Junyu Zhang(junyuzprinceton.edu) Lin Xiao(linxfb.com) Abstract: We consider the problem of minimizing 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 optimization, variance reduction, prox-linear algorithm, sample complexity Category 1: Stochastic Programming Category 2: Nonlinear Optimization Citation: arXiv preprint: arXiv:2004.04357 Download: [PDF]Entry Submitted: 05/13/2021Entry Accepted: 05/14/2021Entry Last Modified: 05/13/2021Modify/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 Optimization Online is supported by the Mathematical Optmization Society.