Abstract
Projection-free optimization via different variants of the Frank-Wolfe (FW), a.k.a. Conditional Gradient method has become one of the cornerstones in optimization for machine learning since in many cases the linear minimization oracle is much cheaper to implement than projections and some sparsity needs to be preserved. In a number of applications, e.g. Poisson inverse problems or quantum state tomography, the loss is given by a self-concordant (SC) function having unbounded curvature, implying absence of theoretical guarantees for the existing FW methods. We use the theory of SC functions to provide a new adaptive step size for FW methods and prove global convergence rate O(1/k) after k iterations. If the problem admits a stronger local linear minimization oracle, we construct a novel FW method with linear convergence rate for SC functions.
Original language | English |
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Title of host publication | Proceedings of the 37th International Conference on Machine Learning |
Publisher | Proceedings of Machine Learning Research |
Pages | 2814-2824 |
Volume | 119 |
Publication status | Published - 2020 |
Event | 37th International Conference on Machine Learning - Virtual Conference Only, Unknown Duration: 12 Jul 2020 → 18 Jul 2020 Conference number: 37 https://icml.cc/Conferences/2020 |
Conference
Conference | 37th International Conference on Machine Learning |
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Abbreviated title | ICML 2020 |
Country/Territory | Unknown |
Period | 12/07/20 → 18/07/20 |
Internet address |