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 characteristic function ($\phi$-function) of a certain ``worst-case'' privacy loss random variable. We show that our approach allows natural adaptive composition like Renyi DP, provides exactly tight privacy accounting like PLD, and can be (often losslessly) converted to privacy profile and $f$-DP, thus providing $(\epsilon,\delta)$-DP guarantees and interpretable tradeoff functions. Algorithmically, we propose an analytical Fourier accountant that represents the 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.

该论文介绍了一种基于特征函数的差分隐私机制，同时提出了解决性能问题的方法，并且通过理论和实验展示了其灵活性和密切相关性。

特征函数在差分隐私最优会计中的应用