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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.
Wang et al. (Tue,) studied this question.