  We adapt a manifold sampling algorithm for the nonsmooth, nonconvex
formulations of learning that arise when imposing robustness to outliers
present in the training data. We demonstrate the approach on objectives based
on trimmed loss. Empirical results show that the method has favorable scaling
properties. Although savings in time come at the expense of not certifying
optimality, the algorithm consistently returns high-quality solutions on the
trimmed linear regression and multiclass classification problems tested.
