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We give the first polynomial-time algorithm for the testable learning ofhalfspaces in the presence of adversarial label noise under the Gaussiandistribution. In the recently introduced testable learning model, one isrequired to produce a tester-learner such that if the data passes the tester,then one can trust the output of the robust learner on the data. Ourtester-learner runs in time $\poly(d/\eps)$ and outputs a halfspace withmisclassification error $O(\opt)+\eps$, where $\opt$ is the 0-1 error of thebest fitting halfspace. At a technical level, our algorithm employs aniterative soft localization technique enhanced with appropriate testers toensure that the data distribution is sufficiently similar to a Gaussian.

Efficient Testable Learning of Halfspaces with Adversarial Label Noise