Adaptive Catalyst for Smooth Convex Optimization
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 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).
Cite
@article{arxiv.1911.11271,
title = {Adaptive Catalyst for Smooth Convex Optimization},
author = {Anastasiya Ivanova and Dmitry Pasechnyuk and Dmitry Grishchenko and Egor Shulgin and Alexander Gasnikov and Vladislav Matyukhin},
journal= {arXiv preprint arXiv:1911.11271},
year = {2021}
}