We give a fast algorithm to optimally compose privacy guarantees of differentially private (DP) algorithms to arbitrary accuracy. Our method is based on the notion of privacy loss random variables to quantify the privacy loss of DP algorithms. The running time and memory needed for our algorithm to approximate the privacy curve of a DP algorithm composed with itself k times is O(k^{1/2}). This improves over the best prior method by Koskela et al. (2020) which requires Ω(k^{1.5}) running time. We demonstrate the utility of our algorithm by accurately computing the privacy loss of DP-SGD algorithm of Abadi et al. (2016) and showing that our algorithm speeds up the privacy computations by a few orders of magnitude compared to prior work, while maintaining similar accuracy.
We have developed a new algorithm to optimally compose privacy guarantees of differentially private (DP) algorithms to arbitrary accuracy. This release accompanies our research paper. We hope to help the privacy community run more accurate accounting of privacy budgets and maintain Microsoft's position in the privacy research field.
