Abstract : We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity operator with respect to the non-smooth term. We show that both the basic proximal-gradient method and the accelerated proximal-gradient method achieve the same convergence rate as in the error-free case, provided that the errors decrease at appropriate rates.Using these rates, we perform as well as or better than a carefully chosen fixed error level on a set of structured sparsity problems.
https://hal.inria.fr/inria-00618152 Contributor : Nicolas Le RouxConnect in order to contact the contributor Submitted on : Thursday, December 1, 2011 - 4:03:15 PM Last modification on : Thursday, March 17, 2022 - 10:08:43 AM Long-term archiving on: : Monday, December 5, 2016 - 12:57:43 AM
Mark Schmidt, Nicolas Le Roux, Francis Bach. Convergence Rates of Inexact Proximal-Gradient Methods for Convex Optimization. NIPS'11 - 25 th Annual Conference on Neural Information Processing Systems, Dec 2011, Grenada, Spain. ⟨inria-00618152v3⟩