Stochastic First- and Zeroth-Order Methods for Nonconvex Stochastic Programming
In this paper, we introduce a new stochastic approximation type algorithm, namely, the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming problems. We establish the complexity of this method for computing an approximat...
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| Published in | SIAM journal on optimization Vol. 23; no. 4; pp. 2341 - 2368 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia
Society for Industrial and Applied Mathematics
01.01.2013
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1052-6234 1095-7189 |
| DOI | 10.1137/120880811 |
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| Abstract | In this paper, we introduce a new stochastic approximation type algorithm, namely, the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming 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 postoptimization phase to evaluate a short list of solutions generated by several independent runs of the RSG method, and we show that such modification allows us 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. [PUBLICATION ABSTRACT] |
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| AbstractList | In this paper, we introduce a new stochastic approximation type algorithm, namely, the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming 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 postoptimization phase to evaluate a short list of solutions generated by several independent runs of the RSG method, and we show that such modification allows us 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. [PUBLICATION ABSTRACT] |
| Author | Ghadimi, Saeed Lan, Guanghui |
| Author_xml | – sequence: 1 givenname: Saeed surname: Ghadimi fullname: Ghadimi, Saeed – sequence: 2 givenname: Guanghui surname: Lan fullname: Lan, Guanghui |
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| ContentType | Journal Article |
| Copyright | 2013, Society for Industrial and Applied Mathematics |
| Copyright_xml | – notice: 2013, Society for Industrial and Applied Mathematics |
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| References | atypb9 Nesterov Y. E. (atypb25) 1983; 269 atypb19 Mairal J. (atypb21) 2009 atypb27 atypb29 atypb23 atypb40 atypb41 atypb20 Mason L. (atypb22) 1999; 12 atypb37 atypb16 atypb17 atypb18 atypb11 atypb33 atypb14 atypb36 atypb1 atypb3 atypb2 atypb10 atypb32 atypb4 atypb7 atypb6 |
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| Snippet | In this paper, we introduce a new stochastic approximation type algorithm, namely, the randomized stochastic gradient (RSG) method, for solving an important... |
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| SubjectTerms | Algorithms Approximation Methods Optimization Random variables Simulation |
| Title | Stochastic First- and Zeroth-Order Methods for Nonconvex Stochastic Programming |
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