Fast column generation for atomic norm regularization
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Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54:547556, 2017.
Abstract
We consider optimization problems that consist in minimizing a quadratic function under an atomic norm regularization or constraint. In the line of work on conditional gradient algorithms, we show that the fully corrective FrankWolfe (FCFW) algorithm — which is most naturally reformulated as a column generation algorithm in the regularized case — can be made particularly efficient for difficult problems in this family by solving the simplicial or conical subproblems produced by FCFW using a special instance of a classical active set algorithm for quadratic programming that generalizes the minnorm point algorithm.
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