Halfspace learning gets differential privacy for free: in three agnostic settings the privacy cost folds into the statistical term
For agnostically learning halfspaces with arbitrary labels under Gaussian marginals, computationally efficient differentially private algorithms were previously missing. This work reports efficient private learners in three settings, improper, proper and semi-agnostic; when the privacy parameter is at least the accuracy parameter, the extra sample cost of privacy is absorbed by each setting's non-private statistical term, making privacy free in sample complexity.