Computing Differential Privacy Guarantees for Heterogeneous Compositions Using FFT

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 Rényi accountants when applied to homogeneous compositions, i.e., to compositions of identical mechanisms. In this work, we extend this approach to heterogeneous compositions. We carry out a full error analysis that allows choosing the parameters of the algorithm such that a desired accuracy is obtained. The analysis also extends previous results by taking into account all the parameters of the algorithm. 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.