The DOI matches its Crossref record; 40 of the 40 references it cites were found in a registry or an index.
Stochastic Model-Based Minimization of Weakly Convex Functions
Open accessAbstract
We consider a family of algorithms that successively sample and minimize simple stochastic models of the objective function. We show that under reasonable conditions on approximation quality and regularity of the models, any such algorithm drives a natural stationarity measure to zero at the rate $O(k^{-1/4})$. As a consequence, we obtain the first complexity guarantees for the stochastic proximal point, proximal subgradient, and regularized Gauss--Newton methods for minimizing compositions of convex functions with smooth maps. The guiding principle, underlying the complexity guarantees, is that all algorithms under consideration can be interpreted as approximate descent methods on an implicit smoothing of the problem, given by the Moreau envelope. Specializing to classical circumstances, we obtain the long-sought convergence rate of the stochastic projected gradient method, without batching, for minimizing a smooth function on a closed convex set.
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Cites
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Robust Stochastic Approximation Approach to Stochastic Programming
Nemirovski, A., Juditsky, A., Lan, G., & Shapiro, A. (2009) · SIAM Journal on Optimization · doi:10.1137/070704277 · Cited by 1,945
Proximité et dualité dans un espace hilbertien
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Stochastic First- and Zeroth-Order Methods for Nonconvex Stochastic Programming
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Cited by
Data-Driven Aerospace Engineering: Reframing the Industry with Machine Learning
Brunton, S. L., Nathan Kutz, J., Manohar, K., Aravkin, A. Y., Morgansen, K., Klemisch, J., Goebel, N., Buttrick, J., Poskin, J., Blom-Schieber, A. W., et al. (2021) · AIAA Journal · doi:10.2514/1.j060131 · Cited by 270
Metadata
- Authors
- Davis, D., & Drusvyatskiy, D.
- Venue
- SIAM Journal on Optimization
- Published
- 2019-01
- Volume
- 29
- Issue
- 1
- Pages
- 207-239
- ISSN
- 1052-6234 (ISSN-L)
- 1095-7189
- OpenAlex
- W2790417304
- Cited by
- 258
- References
- 40
- FWCI
- 15.43
- Type
- journal article
- Language
- en
- Open access
- green
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