Beyond GAP screening for Lasso by exploiting new dual cutting half-spaces with supplementary material
This work addresses computational efficiency for Lasso solvers, which is an incremental improvement in optimization methods for machine learning.
The paper tackles the problem of accelerating Lasso optimization by proposing a novel safe screening test based on a dome geometry and dual cutting half-spaces, which is shown to be more powerful than existing GAP methods and leads to significant speed improvements in numerical experiments.
In this paper, we propose a novel safe screening test for Lasso. Our procedure is based on a safe region with a dome geometry and exploits a canonical representation of the set of half-spaces (referred to as "dual cutting half-spaces" in this paper) containing the dual feasible set. The proposed safe region is shown to be always included in the state-of-the-art "GAP Sphere" and "GAP Dome" proposed by Fercoq et al. (and strictly so under very mild conditions) while involving the same computational burden. Numerical experiments confirm that our new dome enables to devise more powerful screening tests than GAP regions and lead to significant acceleration to solve Lasso.