资源论文On Matching Pursuit and Coordinate Descent

On Matching Pursuit and Coordinate Descent

2020-03-16 | |  79 |   62 |   0

Abstract

Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the latter considers a generalized notion of directions Exploiting the connection between the two algorithms, we present a unified analysis of both, providing affine invariant sublinear 图片.png rates on smooth objectives and linear convergence on strongly convex objectives. As a byproduct of our affine invariant analysis of matching pursuit, our rates for steepest coordinate descent are the tightest known. Furthermore, we show the first accelerated convergence rate 图片.png for matching pursuit and steepest coordinate descent on convex objectives.

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