AISTATS 2017poster71 citations
A Unified Optimization View on Generalized Matching Pursuit and Frank-Wolfe
Francesco Locatello, Rajiv Khanna, Michael Tschannen, Martin Jaggi
Abstract
Two of the most fundamental prototypes of greedy optimization are the matching pursuit and Frank-Wolfe algorithms. In this paper we take a unified view on both classes of methods, leading to the first explicit convergence rates of matching pursuit methods in an optimization sense, for general sets of atoms. We derive sublinear (1/t) convergence for both classes on general smooth objectives, and linear convergence on strongly convex objectives, as well as a clear correspondence of algorithm variants. Our presented algorithms and rates are affine invariant, and do not need any incoherence or sparsity assumptions.
BibTeX
@InProceedings{pmlr-v54-locatello17a,
title = {{A Unified Optimization View on Generalized Matching Pursuit and Frank-Wolfe}},
author = {Locatello, Francesco and Khanna, Rajiv and Tschannen, Michael and Jaggi, Martin},
booktitle = {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics},
pages = {860--868},
year = {2017},
editor = {Singh, Aarti and Zhu, Jerry},
volume = {54},
series = {Proceedings of Machine Learning Research},
month = {20--22 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v54/locatello17a/locatello17a.pdf},
url = {https://proceedings.mlr.press/v54/locatello17a.html},
abstract = {Two of the most fundamental prototypes of greedy optimization are the matching pursuit and Frank-Wolfe algorithms. In this paper we take a unified view on both classes of methods, leading to the first explicit convergence rates of matching pursuit methods in an optimization sense, for general sets of atoms. We derive sublinear (1/t) convergence for both classes on general smooth objectives, and linear convergence on strongly convex objectives, as well as a clear correspondence of algorithm variants. Our presented algorithms and rates are affine invariant, and do not need any incoherence or sparsity assumptions.}
}