论文标题
半空间的私人学习：简化结构并降低样本复杂性
Private Learning of Halfspaces: Simplifying the Construction and Reducing the Sample Complexity
论文作者
论文摘要
我们在$ \ mathbb {r}^d $中为半空间提供了差异私人学习者，带有样本复杂性$ \ of d d^{2.5} \ cdot 2^{\ log log^*| g |} $，它改善了[beimel et a $ d^$ d^2^2^2^2^2^2^2^2.我们的学习者的构建块是一种用于近似解决线性可行性问题的新的差异私有算法：给定表单$ ax \ geq b $的$ m $线性约束的可行集合，其任务是私下确定满足大多数约束的解决方案$ x $。我们的算法是迭代的，每个迭代都会确定构造解决方案$ x $的下一个坐标。
We present a differentially private learner for halfspaces over a finite grid $G$ in $\mathbb{R}^d$ with sample complexity $\approx d^{2.5}\cdot 2^{\log^*|G|}$, which improves the state-of-the-art result of [Beimel et al., COLT 2019] by a $d^2$ factor. The building block for our learner is a new differentially private algorithm for approximately solving the linear feasibility problem: Given a feasible collection of $m$ linear constraints of the form $Ax\geq b$, the task is to privately identify a solution $x$ that satisfies most of the constraints. Our algorithm is iterative, where each iteration determines the next coordinate of the constructed solution $x$.
