Stochastic Frank-Wolfe for Constrained Finite-Sum Minimization

Geoffrey Negiar · Gideon Dresdner · Alicia Yi-Ting Tsai · Laurent El Ghaoui · Francesco Locatello · Robert Freund · Fabian Pedregosa

Keywords: [ Convex Optimization ] [ Large Scale Learning and Big Data ] [ Sparsity and Compressed Sensing ] [ Optimization - Convex ]

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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.

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