Stochastic Frank-Wolfe for Constrained Finite-Sum Minimization
Geoffrey Negiar, Gideon Dresdner, Alicia Tsai, Laurent El Ghaoui, Francesco Locatello, Robert Freund, Fabian Pedregosa
Abstract
We propose a novel Stochastic Frank-Wolfe (a. k. a. conditional gradient) algorithm for constrained smooth finite-sum minimization with a generalized linear prediction/structure. This class of problems includes empirical risk minimization with sparse, low-rank, or other structured constraints. The proposed method is simple to implement, does not require step-size tuning, and has a constant per-iteration cost that is independent of the dataset size. Furthermore, as a byproduct of the method we obtain a stochastic estimator of the Frank-Wolfe gap that can be used as a stopping criterion. Depending on the setting, the proposed method matches or improves on the best computational guarantees for Stochastic Frank-Wolfe algorithms. Benchmarks on several datasets highlight different regimes in which the proposed method exhibits a faster empirical convergence than related methods. Finally, we provide an implementation of all considered methods in an open-source package.
BibTeX
@InProceedings{pmlr-v119-negiar20a,
title = {Stochastic Frank-{W}olfe for Constrained Finite-Sum Minimization},
author = {Negiar, Geoffrey and Dresdner, Gideon and Tsai, Alicia and Ghaoui, Laurent El and Locatello, Francesco and Freund, Robert and Pedregosa, Fabian},
booktitle = {Proceedings of the 37th International Conference on Machine Learning},
pages = {7253--7262},
year = {2020},
editor = {III, Hal Daumé and Singh, Aarti},
volume = {119},
series = {Proceedings of Machine Learning Research},
month = {13--18 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v119/negiar20a/negiar20a.pdf},
url = {https://proceedings.mlr.press/v119/negiar20a.html},
abstract = {We propose a novel Stochastic Frank-Wolfe (a. k. a. conditional gradient) algorithm for constrained smooth finite-sum minimization with a generalized linear prediction/structure. This class of problems includes empirical risk minimization with sparse, low-rank, or other structured constraints. The proposed method is simple to implement, does not require step-size tuning, and has a constant per-iteration cost that is independent of the dataset size. Furthermore, as a byproduct of the method we obtain a stochastic estimator of the Frank-Wolfe gap that can be used as a stopping criterion. Depending on the setting, the proposed method matches or improves on the best computational guarantees for Stochastic Frank-Wolfe algorithms. Benchmarks on several datasets highlight different regimes in which the proposed method exhibits a faster empirical convergence than related methods. Finally, we provide an implementation of all considered methods in an open-source package.}
}