A Universal Catalyst for First-Order Optimization

Hongzhou Lin 1 Julien Mairal 1 Zaid Harchaoui 2, 1
1 LEAR - Learning and recognition in vision
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : We introduce a generic scheme for accelerating first-order optimization methods in the sense of Nesterov, which builds upon a new analysis of the accelerated proximal point algorithm. Our approach consists of minimizing a convex objective by approximately solving a sequence of well-chosen auxiliary problems, leading to faster convergence. This strategy applies to a large class of algorithms, including gradient descent, block coordinate descent, SAG, SAGA, SDCA, SVRG, Finito/MISO, and their proximal variants. For all of these methods, we provide acceleration and explicit support for non-strongly convex objectives. In addition to theoretical speed-up, we also show that acceleration is useful in practice, especially for ill conditioned problems where we measure significant improvements.
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Hongzhou Lin, Julien Mairal, Zaid Harchaoui. A Universal Catalyst for First-Order Optimization. NIPS - Advances in Neural Information Processing Systems, Dec 2015, Montreal, Canada. pp. 3384-3392. ⟨hal-01160728v2⟩

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