Stochastic Frank-Wolfe for Composite Convex Minimization

arXiv1901.10348MaRDI QIDQ6313236

Olivier Fercoq, Alp Yurtsever, Francesco Locatello, Volkan Cevher

Publication date: 29 January 2019

Abstract: A broad class of convex optimization problems can be formulated as a semidefinite program (SDP), minimization of a convex function over the positive-semidefinite cone subject to some affine constraints. The majority of classical SDP solvers are designed for the deterministic setting where problem data is readily available. In this setting, generalized conditional gradient methods (aka Frank-Wolfe-type methods) provide scalable solutions by leveraging the so-called linear minimization oracle instead of the projection onto the semidefinite cone. Most problems in machine learning and modern engineering applications, however, contain some degree of stochasticity. In this work, we propose the first conditional-gradient-type method for solving stochastic optimization problems under affine constraints. Our method guarantees $mathcalO(k^{-1/3})$ convergence rate in expectation on the objective residual and $mathcalO(k^{-5/12})$ on the feasibility gap.

Has companion code repository: https://github.com/alpyurtsever/SHCGM

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