  This paper studies binary classification in robust one-bit compressed sensing
with adversarial errors. It is assumed that the model is overparameterized and
that the parameter of interest is effectively sparse. AdaBoost is considered,
and, through its relation to the max-$\ell_1$-margin-classifier, prediction
error bounds are derived. The developed theory is general and allows for
heavy-tailed feature distributions, requiring only a weak moment assumption and
an anti-concentration condition. Improved convergence rates are shown when the
features satisfy a small deviation lower bound. In particular, the results
provide an explanation why interpolating adversarial noise can be harmless for
classification problems. Simulations illustrate the presented theory.
