The recently proposed Fast Fourier Transform (FFT)-based accountant for evaluating $(\varepsilon,\delta)$-differential privacy guarantees using the privacy loss distribution formalism has been shown to give tighter bounds than commonly used methods such as R\'enyi accountants when applied to compositions of homogeneous mechanisms. This approach is also applicable to certain discrete mechanisms that cannot be analysed with R\'enyi accountants. In this paper, we extend this approach to compositions of heterogeneous mechanisms. We carry out a full error analysis that allows choosing the parameters of the algorithm such that a desired accuracy is obtained. Using our analysis, we also give a bound for the computational complexity in terms of the error which is analogous to and slightly tightens the one given by Murtagh and Vadhan (2018). We also show how to speed up the evaluation of tight privacy guarantees using the Plancherel theorem at the cost of increased pre-computation and memory usage.

本文将最近提出的基于快速傅里叶变换（FFT）的隐私保证算法扩展到异构组合，并进行了完整的误差分析以选择算法参数，进一步提高了差分隐私保证精度，并使用Plancherel定理加速算法。

使用快速傅里叶变换计算异构组合的差分隐私保证