  We derive the optimal differential privacy (DP) parameters of a mechanism
that satisfies a given level of R\'enyi differential privacy (RDP). Our result
is based on the joint range of two $f$-divergences that underlie the
approximate and the R\'enyi variations of differential privacy. We apply our
result to the moments accountant framework for characterizing privacy
guarantees of stochastic gradient descent. When compared to the
state-of-the-art, our bounds may lead to about 100 more stochastic gradient
descent iterations for training deep learning models for the same privacy
budget.
