Agnostic Proper Learning of Halfspaces under Gaussian Marginals
This addresses a fundamental challenge in machine learning for robust classification under noise, offering practical improvements for applications requiring proper models, though it is incremental in building on prior improper methods.
The paper tackles the problem of agnostically learning halfspaces under Gaussian distributions, achieving the first proper learning algorithm with sample and computational complexity matching the best known improper learner, and also provides the first proper polynomial-time approximation scheme for homogeneous halfspaces.
We study the problem of agnostically learning halfspaces under the Gaussian distribution. Our main result is the {\em first proper} learning algorithm for this problem whose sample complexity and computational complexity qualitatively match those of the best known improper agnostic learner. Building on this result, we also obtain the first proper polynomial-time approximation scheme (PTAS) for agnostically learning homogeneous halfspaces. Our techniques naturally extend to agnostically learning linear models with respect to other non-linear activations, yielding in particular the first proper agnostic algorithm for ReLU regression.