Efficient Testable Learning of General Halfspaces with Adversarial Label Noise

TL;DR

This paper introduces the first polynomial-time tester-learner for general halfspaces with adversarial label noise, achieving dimension-independent error, and employs a novel reduction to nearly homogeneous halfspaces.

Contribution

It presents a new polynomial-time tester-learner for general halfspaces under adversarial noise, with a reduction technique to nearly homogeneous cases.

Findings

Achieves dimension-independent misclassification error.

First polynomial-time solution for testable learning of general halfspaces.

Introduces a new reduction methodology for testable learning.

Abstract

We study the task of testable learning of general -- not necessarily homogeneous -- halfspaces with adversarial label noise with respect to the Gaussian distribution. In the testable learning framework, the goal is to develop a tester-learner such that if the data passes the tester, then one can trust the output of the robust learner on the data.Our main result is the first polynomial time tester-learner for general halfspaces that achieves dimension-independent misclassification error. At the heart of our approach is a new methodology to reduce testable learning of general halfspaces to testable learning of nearly homogeneous halfspaces that may be of broader interest.