Robustly Learning a Single Neuron via Sharpness
Robustly Learning a Single Neuron via Sharpness
复制标题
DOI：
10.48550/arxiv.2306.07892
复制
发表时间：
2023-06
期刊：
影响因子：
--
通讯作者：
Puqian Wang;Nikos Zarifis;Ilias Diakonikolas;Jelena Diakonikolas
中科院分区：
文献类型：
--
作者：
Puqian Wang;Nikos Zarifis;Ilias Diakonikolas;Jelena Diakonikolas
我们研究了在存在对抗标签噪声的情况下，学习相对于$ L_2^2 $ -LOSS的单个神经元的问题。我们给出了一种有效的算法，对于包括Relus在内的广泛激活系列，它近似于最佳的$ L_2^2 $ -ERROR在恒定因素内。与先前的工作相比，我们的算法适用于较温和的分布假设。使我们的结果的关键要素是优化理论与局部误差界限的新联系。
We study the problem of learning a single neuron with respect to the $L_2^2$-loss in the presence of adversarial label noise. We give an efficient algorithm that, for a broad family of activations including ReLUs, approximates the optimal $L_2^2$-error within a constant factor. Our algorithm applies under much milder distributional assumptions compared to prior work. The key ingredient enabling our results is a novel connection to local error bounds from optimization theory.