Characterizing the privacy degradation over compositions, i.e., privacy accounting, is a fundamental topic in differential privacy (DP) with many applications to differentially private machine learning and federated learning. We propose a unification of recent advances (Renyi DP, privacy profiles, $f$-DP and the PLD formalism) via the \emph{characteristic function} ($\phi$-function) of a certain \emph{dominating} privacy loss random variable. We show that our approach allows \emph{natural} adaptive composition like Renyi DP, provides \emph{exactly tight} privacy accounting like PLD, and can be (often \emph{losslessly}) converted to privacy profile and $f$-DP, thus providing $(\epsilon,\delta)$-DP guarantees and interpretable tradeoff functions. Algorithmically, we propose an \emph{analytical Fourier accountant} that represents the \emph{complex} logarithm of $\phi$-functions symbolically and uses Gaussian quadrature for numerical computation. On several popular DP mechanisms and their subsampled counterparts, we demonstrate the flexibility and tightness of our approach in theory and experiments.

翻译：隐私在构成上的退化, 即隐私会计, 是不同隐私(DP)中的一个基本主题, 有很多不同的私人机器学习和联合学习的应用。 我们提议通过某种隐私损失随机变量的\ emph{ 属性函数( phim$- 函数) 来统一最近的进展( Renyi DP、 隐私剖面、 $f- DP 和 PLD 形式主义 ), 从而提供$( epsilon,\ delta) $- DP 的保证和可解释的交易功能。 我们提议使用一个 emph{ 分析性 Fourier 会计师}, 代表 Renyi DP, 提供像 PLD 那样的隐私会计, 提供\ emphy{ exactly clotive} 隐私会计会计会计, 提供像 PLD, 可以( 通常\ emph{ lossunly} ) 转换为隐私配置和 $flex- DP 格式化, 从而提供( exphyalive) $- $- preficreal) 和 DP imalationalationalationalational 和 imaltiquestationalationals 和 expalationalationals 和 imalupal- 等等的对等模型, 。