Private Learning of Halfspaces: Simplifying the Construction and Reducing the Sample Complexity
Private Learning of Halfspaces: Simplifying the Construction and Reducing the Sample Complexity
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半空间的私人学习：简化构建并降低样本复杂度
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Eliad Tsfadia
中科院分区：
文献类型：
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作者：
Haim Kaplan;Y. Mansour;Uri Stemmer;Eliad Tsfadia
我们在$ \ mathbb {r}^d $ in Sample Complectity $ \ lot d d^{2.5} \ cdot 2^{\ log log^*| g |} $上提出了一个有限网格$ g $ in $ \ mathbb {r}^d $ in $ \ mathbb {r}^d $ in $ \ mathbb {r}^d $中的差异私人学习者，这将[Beimel等人，Colt 2019]的最新结果提高了$ d^2 $。我们学习者的构建块是一种用于近似解决线性可行性问题的新的差异私有算法：给定表单$ ax \ geq b $的$ m $线性约束的可行集合，其任务是私下识别解决方案$ x满足大多数约束的$。我们的算法是迭代的，每个迭代都会确定构造解决方案$ 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 $x$.
DOI：
10.1145/3188745.3188946
发表时间：
2018-06
期刊：
Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing
影响因子：
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作者：
Mark Bun;C. Dwork;G. Rothblum;T. Steinke
通讯作者：
Mark Bun;C. Dwork;G. Rothblum;T. Steinke
私有中心点和半空间学习
DOI：
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发表时间：
2020
期刊：
COLT 2019
影响因子：
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作者：
Amos Beimel, Shay Moran
通讯作者：
Amos Beimel, Shay Moran