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Convergence Rates of Inexact Proximal-Gradient Methods for Convex Optimization
Mark Schmidt · Nicolas Le Roux · Francis Bach

Wed Dec 14 08:45 AM -- 02:59 PM (PST) @ None #None

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 second term. We show that the basic proximal-gradient method, the basic proximal-gradient method with a strong convexity assumption, and the accelerated proximal-gradient method achieve the same convergence rates as in the error-free case, provided the errors decrease at an appropriate rate. Our experimental results on a structured sparsity problem indicate that sequences of errors with these appealing theoretical properties can lead to practical performance improvements.

Author Information

Mark Schmidt (INRIA - SIERRA Project Team)
Nicolas Le Roux (Google AI)
Francis Bach (INRIA - Ecole Normale Superieure)

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