Subsampled R\\'enyi Differential Privacy and Analytical Moments Accountant

We study the problem of subsampling in differential privacy (DP), a question is the centerpiece behind many successful differentially private machine algorithms. Specifically, we provide a tight upper bound on the\\'enyi Differential Privacy (RDP) (Mironov, 2017) parameters for algorithms: (1) subsample the dataset, and then (2) applies a randomized mechanism M the subsample, in terms of the RDP parameters of M and the subsampling parameter. Our results generalize the moments accounting technique, by Abadi et al. (2016) for the Gaussian mechanism, to any subsampled mechanism.