Adaptive Catalyst for Smooth Convex Optimization

Anastasiya Ivanova; Dmitry Pasechnyuk; Dmitry Grishchenko; Egor Shulgin; Alexander Gasnikov; Vladislav Matyukhin

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arXiv · 1911.11271

Adaptive Catalyst for Smooth Convex Optimization

Anastasiya Ivanova·Dmitry Pasechnyuk·Dmitry Grishchenko·Egor Shulgin·Alexander Gasnikov·Vladislav Matyukhin

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Abstract

In this paper, we present a generic framework that allows accelerating almost arbitrary non-accelerated deterministic and randomized algorithms for smooth convex optimization problems. The main approach of our envelope is the same as in Catalyst (Lin et al., 2015): an accelerated proximal outer gradient method, which is used as an envelope for a non-accelerated inner method for the $\ell_2$ regularized auxiliary problem. Our algorithm has two key differences: 1) easily verifiable stopping criteria for inner algorithm; 2) the regularization parameter can be tunned along the way. As a result, the main contribution of our work is a new framework that applies to adaptive inner algorithms: Steepest Descent, Adaptive Coordinate Descent, Alternating Minimization. Moreover, in the non-adaptive case, our approach allows obtaining Catalyst without a logarithmic factor, which appears in the standard Catalyst (Lin et al., 2015, 2018).

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Anastasiya Ivanova, Dmitry Pasechnyuk, Dmitry Grishchenko, Egor Shulgin, Alexander Gasnikov, Vladislav Matyukhin. 2019-11-25. Adaptive Catalyst for Smooth Convex Optimization. https://arxiv.org/abs/1911.11271

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