Stochastic Three-Composite Convex Minimization with a Linear Operator

Renbo Zhao, Volkan Cevher
Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:765-774, 2018.

Abstract

We develop a primal-dual convex minimization framework to solve a class of stochastic convex three-composite problem with a linear operator. We consider the cases where the problem is both convex and strongly convex and analyze the convergence of the proposed algorithm in both cases. In addition, we extend the proposed framework to deal with additional constraint sets and multiple non-smooth terms. We provide numerical evidence on graph-guided sparse logistic regression, fused lasso and overlapped group lasso, to demonstrate the superiority of our approach to the state-of-the-art.

Cite this Paper

BibTeX
@InProceedings{pmlr-v84-zhao18a, title = {Stochastic Three-Composite Convex Minimization with a Linear Operator}, author = {Zhao, Renbo and Cevher, Volkan}, booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics}, pages = {765--774}, year = {2018}, editor = {Storkey, Amos and Perez-Cruz, Fernando}, volume = {84}, series = {Proceedings of Machine Learning Research}, month = {09--11 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v84/zhao18a/zhao18a.pdf}, url = {https://proceedings.mlr.press/v84/zhao18a.html}, abstract = {We develop a primal-dual convex minimization framework to solve a class of stochastic convex three-composite problem with a linear operator. We consider the cases where the problem is both convex and strongly convex and analyze the convergence of the proposed algorithm in both cases. In addition, we extend the proposed framework to deal with additional constraint sets and multiple non-smooth terms. We provide numerical evidence on graph-guided sparse logistic regression, fused lasso and overlapped group lasso, to demonstrate the superiority of our approach to the state-of-the-art.} }
Endnote
%0 Conference Paper %T Stochastic Three-Composite Convex Minimization with a Linear Operator %A Renbo Zhao %A Volkan Cevher %B Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2018 %E Amos Storkey %E Fernando Perez-Cruz %F pmlr-v84-zhao18a %I PMLR %P 765--774 %U https://proceedings.mlr.press/v84/zhao18a.html %V 84 %X We develop a primal-dual convex minimization framework to solve a class of stochastic convex three-composite problem with a linear operator. We consider the cases where the problem is both convex and strongly convex and analyze the convergence of the proposed algorithm in both cases. In addition, we extend the proposed framework to deal with additional constraint sets and multiple non-smooth terms. We provide numerical evidence on graph-guided sparse logistic regression, fused lasso and overlapped group lasso, to demonstrate the superiority of our approach to the state-of-the-art.
APA
Zhao, R. & Cevher, V.. (2018). Stochastic Three-Composite Convex Minimization with a Linear Operator. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 84:765-774 Available from https://proceedings.mlr.press/v84/zhao18a.html.

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