  Gradient boosting performs exceptionally in most prediction problems and
scales well to large datasets. In this paper we prove that a ``lassoed''
gradient boosted tree algorithm with early stopping achieves faster than
$n^{-1/4}$ L2 convergence in the large nonparametric space of cadlag functions
of bounded sectional variation. This rate is remarkable because it does not
depend on the dimension, sparsity, or smoothness. We use simulation and real
data to confirm our theory and demonstrate empirical performance and
scalability on par with standard boosting. Our convergence proofs are based on
a novel, general theorem on early stopping with empirical loss minimizers of
nested Donsker classes.
