Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming
In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems. We establish the complexity of this method for computing an approximate stationary point of a nonlinear programming problem. We also show that this method possesses a nearly optimal rate of convergence if the problem is convex. We discuss a variant of the algorithm which consists of applying a post-optimization phase to evaluate a short list of solutions generated by several independent runs of the RSG method, and show that such modification allows to improve significantly the large-deviation properties of the algorithm. These methods are then specialized for solving a class of simulation-based optimization problems in which only stochastic zeroth-order information is available.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Zeroth-Order Nonconvex Nonsmooth Optimization with Heavy-Tailed Noise
This paper considers the nonconvex nonsmooth problem in which the objective function is Lipschitz continuous. We focus on the stochastic setting where the algorithm can access stochastic function value evaluations with h…
Zeroth-Order primal-dual Alternating Projection Gradient Algorithms for Nonconvex Minimax Problems with Coupled linear Constraints
In this paper, we study zeroth-order algorithms for nonconvex minimax problems with coupled linear constraints under the deterministic and stochastic settings, which have attracted wide attention in machine learning, sig…
Faster Gradient-Free Proximal Stochastic Methods for Nonconvex Nonsmooth Optimization
Proximal gradient method has been playing an important role to solve many machine learning tasks, especially for the nonsmooth problems. However, in some machine learning problems such as the bandit model and the black-b…
BIG-bench Machine LearningZeroth-order Nonconvex Stochastic Optimization: Handling Constraints, High-Dimensionality and Saddle-Points
In this paper, we propose and analyze zeroth-order stochastic approximation algorithms for nonconvex and convex optimization, with a focus on addressing constrained optimization, high-dimensional setting and saddle-point…
Stochastic OptimizationVocal Bursts Intensity PredictionZeroth-order (Non)-Convex Stochastic Optimization via Conditional Gradient and Gradient Updates
In this paper, we propose and analyze zeroth-order stochastic approximation algorithms for nonconvex and convex optimization. Specifically, we propose generalizations of the conditional gradient algorithm achieving rates…
Stochastic Optimization