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arXiv · 1611.08022

A Stronger Convergence Result on the Proximal Incremental Aggregated Gradient Method

Nuri Denizcan Vanli·Mert Gurbuzbalaban·Asu Ozdaglar
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Abstract

We study the convergence rate of the proximal incremental aggregated gradient (PIAG) method for minimizing the sum of a large number of smooth component functions (where the sum is strongly convex) and a non-smooth convex function. At each iteration, the PIAG method moves along an aggregated gradient formed by incrementally updating gradients of component functions at least once in the last $K$ iterations and takes a proximal step with respect to the non-smooth function. We show that the PIAG algorithm attains an iteration complexity that grows linear in the condition number of the problem and the delay parameter $K$. This improves upon the previously best known global linear convergence rate of the PIAG algorithm in the literature which has a quadratic dependence on $K$.

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Nuri Denizcan Vanli, Mert Gurbuzbalaban, Asu Ozdaglar. 2016-11-23. A Stronger Convergence Result on the Proximal Incremental Aggregated Gradient Method. https://arxiv.org/abs/1611.08022

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