We give an algorithm that learns arbitrary Boolean functions of $k$ arbitrary halfspaces over $\mathbb{R}^n$, in the challenging distribution-free Probably Approximately Correct (PAC) learning model, running in time $2^{\sqrt{n} \cdot (\log n)^{O(k)}}$. This is the first algorithm that can PAC learn even intersections of two halfspaces in time $2^{o(n)}.$

翻译：我们提出了一种算法，能够在具有挑战性的无分布概率近似正确（PAC）学习模型中，学习 $\mathbb{R}^n$ 上 $k$ 个任意半空间的任意布尔函数，运行时间为 $2^{\sqrt{n} \cdot (\log n)^{O(k)}}$。这是首个能够在 $2^{o(n)}$ 时间内PAC学习甚至两个半空间交集的算法。