Abstract

The Group-Lasso is a well-known tool for joint regularization in machine learning methods. While the and the version have been studied in detail and efficient algorithms exist, there are still open questions regarding other variants. We characterize conditions for solutions of the GroupLasso for all p-norms with and we present a unified active set algorithm. For all p-norms, a highly efficient projected gradient algorithm is presented. This new algorithm enables us to compare the prediction performance of many variants of the GroupLasso in a multi-task learning setting, where the aim is to solve many learning problems in parallel which are coupled via the GroupLasso constraint. We conduct large-scale experiments on synthetic data and on two realworld data sets. In accordance with theoretical characterizations of the different norms we observe that the weak-coupling norms with p between 1.5 and 2 consistently outperform the strong-coupling norms with