  We present an oracle-efficient algorithm for boosting the adversarial
robustness of barely robust learners. Barely robust learning algorithms learn
predictors that are adversarially robust only on a small fraction $\beta \ll 1$
of the data distribution. Our proposed notion of barely robust learning
requires robustness with respect to a "larger" perturbation set; which we show
is necessary for strongly robust learning, and that weaker relaxations are not
sufficient for strongly robust learning. Our results reveal a qualitative and
quantitative equivalence between two seemingly unrelated problems: strongly
robust learning and barely robust learning.
