The DOI matches its Crossref record; 31 of the 31 references it cites were found in a registry or an index.
A Proximal Stochastic Gradient Method with Progressive Variance Reduction
Open accessAbstract
We consider the problem of minimizing the sum of two convex functions: one is the average of a large number of smooth component functions, and the other is a general convex function that admits a simple proximal mapping. We assume the whole objective function is strongly convex. Such problems often arise in machine learning, known as regularized empirical risk minimization. We propose and analyze a new proximal stochastic gradient method, which uses a multistage scheme to progressively reduce the variance of the stochastic gradient. While each iteration of this algorithm has similar cost as the classical stochastic gradient method (or incremental gradient method), we show that the expected objective value converges to the optimum at a geometric rate. The overall complexity of this method is much lower than both the proximal full gradient method and the standard proximal stochastic gradient method.
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The Elements of Statistical Learning
Hastie, T., Tibshirani, R., & Friedman, J. (2009) · Springer Series in Statistics · doi:10.1007/978-0-387-84858-7 · Cited by 25,970
The Elements of Statistical Learning
Hastie, T., Friedman, J., & Tibshirani, R. (2001) · Springer Series in Statistics · doi:10.1007/978-0-387-21606-5 · Cited by 24,162
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
Beck, A., & Teboulle, M. (2009) · SIAM Journal on Imaging Sciences · doi:10.1137/080716542 · Cited by 11,952
Introductory Lectures on Convex Optimization: A Basic Course
Nesterov, Y. E. (2014) · Medical Entomology and Zoology · Cited by 3,557
Introductory Lectures on Convex Optimization
Nesterov, Y. (2004) · Applied Optimization · doi:10.1007/978-1-4419-8853-9 · Cited by 2,698
RCV1: A New Benchmark Collection for Text Categorization Research
Lewis, D., Yang, Y., Rose, T. G., & Li, F. (2004) · Goldsmiths (University of London) · doi:10.5555/1005332.1005345 · Cited by 2,503
Splitting Algorithms for the Sum of Two Nonlinear Operators
Lions, P. L., & Mercier, B. (1979) · SIAM Journal on Numerical Analysis · doi:10.1137/0716071 · Cited by 1,972
Accelerating Stochastic Gradient Descent using Predictive Variance Reduction
Johnson, R., & Zhang, T. (2013) · Cited by 1,889
Self-citationGradient methods for minimizing composite functions
Nesterov, Y. (2013) · Mathematical Programming · doi:10.1007/s10107-012-0629-5 · Cited by 1,298
A Modified Forward-Backward Splitting Method for Maximal Monotone Mappings
Tseng, P. (2000) · SIAM Journal on Control and Optimization · doi:10.1137/s0363012998338806 · Cited by 1,223
Cited by
SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives
Defazio, A., Bach, F., & Lacoste-Julien, S. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1407.0202 · Cited by 834
Tank, A., Covert, I., Foti, N., Shojaie, A., & Fox, E. B. (2021) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2021.3065601 · Cited by 282
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
- Xiao, L., & Zhang, T.
- Venue
- SIAM Journal on Optimization
- Published
- 2014-01
- Volume
- 24
- Issue
- 4
- Pages
- 2057-2075
- ISSN
- 1052-6234 (ISSN-L)
- 1095-7189
- OpenAlex
- W2047152541
- Cited by
- 592
- References
- 31
- FWCI
- 60.74
- Type
- journal article
- Language
- en
- Open access
- green
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