Differential privacy (DP) is obtained by randomizing a data analysis algorithm, which necessarily introduces a tradeoff between its utility and privacy. Many DP mechanisms are built upon one of two underlying tools: Laplace and Gaussian additive noise mechanisms. We expand the search space of algorithms by investigating the Generalized Gaussian (GG) mechanism, which samples the additive noise term $x$ with probability proportional to $e^{-\frac{| x |}σ^β }$ for some $β\geq 1$ (denoted $GG_{β, σ}(f,D)$). The Laplace and Gaussian mechanisms are special cases of GG for $β=1$ and $β=2$, respectively. We prove that the full GG family satisfies differential privacy and extend the PRV accountant to support privacy loss computation for these mechanisms. We then instantiate the GG mechanism in two canonical private learning pipelines, PATE and DP-SGD. Empirically, we explore PATE and DP-SGD with the GG mechanism across the computationally feasible values of $β$: $β\in [1,2]$ for DP-SGD and $β\in [1,4]$ for PATE. For both mechanisms, we find that $β=2$ (Gaussian) performs as well as or better than other values in their computational tractable domains.This provides justification for the widespread adoption of the Gaussian mechanism in DP learning.

翻译：差分隐私通过随机化数据分析算法实现，这必然在算法效用与隐私性之间引入权衡。许多差分隐私机制建立于两种基础工具之上：拉普拉斯加性噪声机制与高斯加性噪声机制。我们通过研究广义高斯机制来拓展算法搜索空间，该机制以正比于 $e^{-\frac{| x |}σ^β }$ 的概率采样加性噪声项 $x$（其中 $β\geq 1$，记为 $GG_{β, σ}(f,D)$）。拉普拉斯机制与高斯机制分别是广义高斯机制在 $β=1$ 和 $β=2$ 时的特例。我们证明完整的广义高斯机制族满足差分隐私，并将隐私损失随机变量核算方法扩展至支持此类机制的隐私损失计算。随后，我们将广义高斯机制实例化应用于两种经典隐私学习框架：PATE 和 DP-SGD。通过实验，我们探索了在计算可行取值范围内（DP-SGD 中 $β\in [1,2]$，PATE 中 $β\in [1,4]$）采用广义高斯机制的 PATE 与 DP-SGD 方法。对于两种机制，我们发现在其计算可处理域内，$β=2$（高斯机制）的表现均不劣于甚至优于其他取值。这为高斯机制在差分隐私学习中的广泛采用提供了理论依据。