Before revision:  It has been shown for the case of ridge regression (  p,q,r,s=2) that we can obtain a coreset  smaller than the coreset for its unregularized counterpart i.e. least squares regression (Avron et al.).
After revision:  Prior work has shown that for ridge regression ( p,q,r,s=2) that we can obtain a coreset smaller than the coreset for its unregularized counterpart i.e. least squares regression (Avron et al.).