The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Stochastic First- and Zeroth-Order Methods for Nonconvex Stochastic Programming
Open accessAbstract
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.
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Cites
A Stochastic Approximation Method
Robbins, H., & Monro, S. (1951) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177729586 · Cited by 9,643
Acceleration of Stochastic Approximation by Averaging
Polyak, B. T., & Juditsky, A. B. (1992) · SIAM Journal on Control and Optimization · doi:10.1137/0330046 · Cited by 1,827
An optimal method for stochastic composite optimization
Lan, G. (2012) · Mathematical Programming · doi:10.1007/s10107-010-0434-y · Cited by 427
Self-citation
Cited by
Federated Optimization in Heterogeneous Networks
Li, T., Sahu, A. K., Zaheer, M., Sanjabi, M., Talwalkar, A., & Smith, V. (2018) · arXiv · doi:10.48550/arxiv.1812.06127 · Cited by 4,023
AutoZOOM: Autoencoder-Based Zeroth Order Optimization Method for Attacking Black-Box Neural Networks
Tu, C.-C., Ting, P., Chen, P.-Y., Liu, S., Zhang, H., Yi, J., Hsieh, C.-J., & Cheng, S.-M. (2019) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v33i01.3301742 · Cited by 361
Asynchronous Parallel Stochastic Gradient for Nonconvex Optimization
Lian, X., Huang, Y., Li, Y., & Liu, J. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1506.08272 · Cited by 324
Stochastic Model-Based Minimization of Weakly Convex Functions
Davis, D., & Drusvyatskiy, D. (2019) · SIAM Journal on Optimization · doi:10.1137/18m1178244 · Cited by 258
Riemannian SVRG: Fast Stochastic Optimization on Riemannian Manifolds
Zhang, H., Reddi, S. J., & Sra, S. (2016) · arXiv · doi:10.48550/arxiv.1605.07147 · Cited by 140
Metadata
- Authors
- Ghadimi, S., & Lan, G.
- Venue
- SIAM Journal on Optimization
- Published
- 2013-01
- Volume
- 23
- Issue
- 4
- Pages
- 2341-2368
- ISSN
- 1052-6234 (ISSN-L)
- 1095-7189
- OpenAlex
- W2963470657
- Cited by
- 1,034
- References
- 3
- FWCI
- 15.83
- Type
- journal article
- Language
- en
- Open access
- green
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