  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 $p\textless{}1$. 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.
