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