Feature selection in learning to rank has recently emerged as a crucial issue. Whereas several preprocessing approaches have been proposed, only a few works have been focused on integrating the feature selection into the learning process. In this work, we propose a general framework for feature selection in learning to rank using SVM with a sparse regularization term. We investigate both classical convex regularizations such as $ell_1$ or weighted $ell_1$ and non-convex regularization terms such as log penalty, Minimax Concave Penalty (MCP) or $ell_p$ pseudo norm with $ptextless{}1$. Two algorithms are proposed, first an accelerated proximal approach for solving the convex problems, second a reweighted $ell_1$ scheme to address the non-convex regularizations. We conduct intensive experiments on nine datasets from Letor 3.0 and Letor 4.0 corpora. Numerical results show that the use of non-convex regularizations we propose leads to more sparsity in the resulting models while prediction performance is preserved. The number of features is decreased by up to a factor of six compared to the $ell_1$ regularization. In addition, the software is publicly available on the web.
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