A Fully Polynomial-Time Algorithm for Robustly Learning Halfspaces over the Hypercube

We give the first fully polynomial-time algorithm for learning halfspaces with respect to the uniform distribution on the hypercube in the presence of contamination, where an adversary may corrupt some fraction of examples and labels arbitrarily. We achieve an error guarantee of ηO(1)+є where η is the noise rate. Such a result was not known even in the agnostic setting, where only labels can be adversarially corrupted. All prior work over the last two decades has a superpolynomial dependence in 1/є or succeeds only with respect to continuous marginals (such as log-concave densities).