Differential privacy (DP) has emerged as a de facto standard privacy notion for a wide range of applications. Since the meaning of data utility in different applications may vastly differ, a key challenge is to find the optimal randomization mechanism, i.e., the distribution and its parameters, for a given utility metric. Existing works have identified the optimal distributions in some special cases, while leaving all other utility metrics (e.g., usefulness and graph distance) as open problems. Since existing works mostly rely on manual analysis to examine the search space of all distributions, it would be an expensive process to repeat such efforts for each utility metric. To address such deficiency, we propose a novel approach that can automatically optimize different utility metrics found in diverse applications under a common framework. Our key idea that, by regarding the variance of the injected noise itself as a random variable, a two-fold distribution may approximately cover the search space of all distributions. Therefore, we can automatically find distributions in this search space to optimize different utility metrics in a similar manner, simply by optimizing the parameters of the two-fold distribution. Specifically, we define a universal framework, namely, randomizing the randomization mechanism of differential privacy (R$^2$DP), and we formally analyze its privacy and utility. Our experiments show that R$^2$DP can provide better results than the baseline distribution (Laplace) for several utility metrics with no known optimal distributions, whereas our results asymptotically approach to the optimality for utility metrics having known optimal distributions. As a side benefit, the added degree of freedom introduced by the two-fold distribution allows R$^2$DP to accommodate the preferences of both data owners and recipients.

中文翻译：

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R$^2$DP：一种用于优化无已知最优分布的效用指标的差分隐私随机化机制的通用和自动化方法

差分隐私 (DP) 已成为广泛应用的事实上的标准隐私概念。由于不同应用中数据效用的含义可能大不相同，一个关键的挑战是为给定的效用度量找到最优的随机化机制，即分布及其参数。现有工作已经确定了某些特殊情况下的最佳分布，而将所有其他效用指标（例如，有用性和图距离）作为开放问题。由于现有工作主要依靠手动分析来检查所有分布的搜索空间，因此为每个效用指标重复此类工作将是一个昂贵的过程。为了解决这种缺陷，我们提出了一种新方法，可以在通用框架下自动优化在不同应用程序中发现的不同效用指标。我们的关键思想是，通过将注入噪声本身的方差视为随机变量，二重分布可以近似覆盖所有分布的搜索空间。因此，我们可以在这个搜索空间中自动找到分布，以类似的方式优化不同的效用指标，只需优化二重分布的参数。具体来说，我们定义了一个通用框架，即对差分隐私（R$^2$DP）的随机化机制进行随机化，并正式分析其隐私和效用。我们的实验表明，对于几个没有已知最优分布的效用指标，R$^2$DP 可以提供比基线分布（拉普拉斯）更好的结果，而我们的结果渐近地接近具有已知最优分布的效用指标的最优性。