Primal-Dual Block Frank-Wolfe

Qi Lei, Jiacheng Zhuo, Inderjit Dhillon, Constantine Caramanis, Alexandros Dimakis

Abstract:   We propose a variant of the Frank-Wolfe algorithm for solving a class of sparse/low-rank optimization problems. Our formulation includes Elastic Net, regularized SVMs and phase retrieval as special cases. The proposed Primal-Dual Block Frank-Wolfe algorithm reduces the per-iteration cost while maintaining linear convergence rate. The per iteration cost of our method depends on the structural complexity of the solution (i.e. sparsity/low-rank) instead of the ambient dimension. We empirically show that our algorithm outperforms the state-of-the-art methods on (multi-class) classification tasks.

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  • Primal-Dual Block Frank-Wolfe (pdf, software)
    Q. Lei, J. Zhuo, I. Dhillon, C. Caramanis, A. Dimakis.
    To appear in Neural Information Processing Systems (NIPS), 2019.