A Better Bound Gives a Hundred Rounds: Enhanced Privacy Guarantees via f-Divergences

We derive the optimal differential privacy (DP) parameters of a mechanism that satisfies a given level of Renyi´ differential privacy (RDP). Our result is based on the joint range of two f-divergences that underlie the approximate and the Renyi 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.