Learning general halfspaces with general Massart noise under the Gaussian distribution

We study the problem of PAC learning halfspaces on R d with Massart noise under the Gaussian distribution. In the Massart model, an adversary is allowed to flip the label of each point x with unknown probability η(x) ≤ η, for some parameter η ∈ [0, 1/2]. The goal of the learner is to output a hypothesis with misclassification error of OPT + ǫ, where OPT is the error of the target halfspace. This problem had been previously studied under two assumptions: (i) the target halfspace is homogeneous (i.e., the separating hyperplane goes through the origin), and (ii) the parameter η is strictly smaller than 1/2. Prior to this work, no nontrivial bounds were known for the general case when either of these assumptions is removed. Here we study the general problem and establish the following results: