arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2302.01855cs.LGstat.ML
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从健壮性到隐私性,再回到

From Robustness to Privacy and Back

Khoury College of Computer Science, Northeastern University(东北大学库利计算机学院);Apple(苹果公司)

Hilal Asi, Jonathan Ullman, Lydia Zakynthinou

摘要:

我们研究了统计推断和机器学习中两个必要的算法之间的关系:差分隐私和对抗性数据损坏的鲁棒性。它们的概念相似性首先由Dwork和Lei(STOC 2009)观察到,他们观察到私有算法满足鲁棒性,并给出了将鲁棒算法转换为私有算法的一般方法。然而,所有用于将鲁棒算法转换为私有算法的一般方法都导致次优的出错率。我们的工作给出了第一个黑盒变换,将任何对抗性强的算法转换为满足纯差分隐私的算法。此外,我们表明,对于任何低维估计任务,将我们的变换应用于最佳鲁棒估计器会产生最佳私人估计器。因此,我们得出结论,对于任何低维任务,$\varepsilon$ -差分私有估计器的最优出错率基本上与对对抗性破坏$1/\varepsilon$训练样本具有鲁棒性的估计器的最优出错率相同。我们应用我们的变换来获得几个高维任务的新的最佳私人估计,包括高斯(稀疏)线性回归和PCA。最后,我们提出了一个扩展我们的转换,导致近似差分隐私算法的误差不依赖于输出空间的范围,这是不可能的纯差分隐私。

英文摘要:

We study the relationship between two desiderata of algorithms in statistical inference and machine learning: differential privacy and robustness to adversarial data corruptions. Their conceptual similarity was first observed by Dwork and Lei (STOC 2009), who observed that private algorithms satisfy robustness, and gave a general method for converting robust algorithms to private ones. However, all general methods for transforming robust algorithms into private ones lead to suboptimal error rates. Our work gives the first black-box transformation that converts any adversarially robust algorithm into one that satisfies pure differential privacy. Moreover, we show that for any low-dimensional estimation task, applying our transformation to an optimal robust estimator results in an optimal private estimator. Thus, we conclude that for any low-dimensional task, the optimal error rate for $\varepsilon$-differentially private estimators is essentially the same as the optimal error rate for estimators that are robust to adversarially corrupting $1/\varepsilon$ training samples. We apply our transformation to obtain new optimal private estimators for several high-dimensional tasks, including Gaussian (sparse) linear regression and PCA. Finally, we present an extension of our transformation that leads to approximate differentially private algorithms whose error does not depend on the range of the output space, which is impossible under pure differential privacy.

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