Learning general halfspaces with general Massart noise under the Gaussian distribution
Ilias Diakonikolas, Daniel M. Kane, Vasilis Kontonis, Christos Tzamos, Nikos Zarifis · 2022
We study the problem of PAC learning halfspaces on ℝd 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 is to find a hypothesis with misclassification error of OPT + є, 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 when either of these assumptions is removed. We study the general problem and establish the following: