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A Universal Catalyst for First-Order Optimization
Hongzhou Lin · Julien Mairal · Zaid Harchaoui

Wed Dec 09 04:00 PM -- 08:59 PM (PST) @ 210 C #87

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.

Author Information

Hongzhou Lin (Inria)
Julien Mairal (INRIA)
Zaid Harchaoui (Inria)

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