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arXiv · 1803.09539

On Matching Pursuit and Coordinate Descent

Francesco Locatello·Anant Raj·Sai Praneeth Karimireddy·Gunnar Rätsch·Bernhard Schölkopf·Sebastian U. Stich·Martin Jaggi
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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 $\mathcal{O}(1/t)$ 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 $\mathcal{O}(1/t^2)$ for matching pursuit and steepest coordinate descent on convex objectives.

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Francesco Locatello, Anant Raj, Sai Praneeth Karimireddy, Gunnar Rätsch, Bernhard Schölkopf, Sebastian U. Stich, Martin Jaggi. 2019-05-31. On Matching Pursuit and Coordinate Descent. https://arxiv.org/abs/1803.09539

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