  Modern technologies are generating ever-increasing amounts of data. Making
use of these data requires methods that are both statistically sound and
computationally efficient. Typically, the statistical and computational aspects
are treated separately. In this paper, we propose an approach to entangle these
two aspects in the context of regularized estimation. Applying our approach to
sparse and group-sparse regression, we show that it can improve on standard
pipelines both statistically and computationally.
