We give the first polynomial-time algorithm for the testable learning of halfspaces in the presence of adversarial label noise under the Gaussian distribution. In the recently introduced testable learning model, one is required 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. Our tester-learner runs in time $\poly(d/\eps)$ and outputs a halfspace with misclassification error $O(\opt)+\eps$, where $\opt$ is the 0-1 error of the best fitting halfspace. At a technical level, our algorithm employs an iterative soft localization technique enhanced with appropriate testers to ensure that the data distribution is sufficiently similar to a Gaussian.

翻译：我们给出了首个多项式时间算法，用于在高斯分布下存在对抗标签噪声时实现半空间的可测试学习。在近期提出的可测试学习模型中，要求生成一个测试学习器，使得若数据通过测试，则可信任该鲁棒学习器在数据上的输出。我们的测试学习器运行时间为 $\poly(d/\eps)$，并输出一个误分类误差为 $O(\opt)+\eps$ 的半空间，其中 $\opt$ 是最优拟合半空间的0-1误差。在技术层面，我们的算法采用了一种迭代软定位技术，并结合适当的测试器，以确保数据分布与高斯分布充分相似。