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Faster One-Sample Stochastic Conditional Gradient Method for Composite Convex Minimization
- Dresdner, Gideon (author)
- Vladarean, Maria-Luiza (author)
- Rätsch, Gunnar (author)
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- Locatello, Francesco (author)
- Cevher, Volkan (author)
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- (creator_code:org_t)
- PMLR, 2022
- 2022
- English.
- In: Proceedings of The 25th International Conference on Artificial Intelligence and Statistics. - : PMLR.
- Conference paper (peer-reviewed)
Abstract
Subject headings
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- We propose a stochastic conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. Existing CGM variants for this template either suffer from slow convergence rates, or require carefully increasing the batch size over the course of the algorithm's execution, which leads to computing full gradients. In contrast, the proposed method, equipped with a stochastic average gradient (SAG) estimator, requires only one sample per iteration. Nevertheless, it guarantees fast convergence rates on par with more sophisticated variance reduction techniques. In applications we put special emphasis on problems with a large number of separable constraints. Such problems are prevalent among semidefinite programming (SDP) formulations arising in machine learning and theoretical computer science. We provide numerical experiments on matrix completion, unsupervised clustering, and sparsest-cut SDPs.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Keyword
- conditional gradient method
- Frank-Wolfe
- convex optimization
- composite optimization
- stochastic optimization
- stochastic constraints
- variance reduction
- stochastic average gradient
- semidefinite programming
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- kon (subject category)
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