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

arXiv: https://arxiv.org/abs/2001.05990 · HTML: https://mlsanity.com/paper/2001.05990/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2020.

## Built on by (most cited first, 21 of 21)

- [Adversary Instantiation: Lower Bounds for Differentially Private Machine Learning](https://mlsanity.com/paper/2101.04535/) (2021)
- [Practical and Private (Deep) Learning without Sampling or Shuffling](https://mlsanity.com/paper/2103.00039/) (2021)
- [How to DP-fy ML: A Practical Guide to Machine Learning with Differential Privacy](https://mlsanity.com/paper/2303.00654/) (2023)
- [The Distributed Discrete Gaussian Mechanism for Federated Learning with Secure Aggregation](https://mlsanity.com/paper/2102.06387/) (2021)
- [The Skellam Mechanism for Differentially Private Federated Learning](https://mlsanity.com/paper/2110.04995/) (2021)
- [Composition of Differential Privacy & Privacy Amplification by Subsampling](https://mlsanity.com/paper/2210.00597/) (2022)
- [Federated Learning with Local Differential Privacy: Trade-offs between Privacy, Utility, and Communication](https://mlsanity.com/paper/2102.04737/) (2021)
- [The Fundamental Price of Secure Aggregation in Differentially Private Federated Learning](https://mlsanity.com/paper/2203.03761/) (2022)
- [Taming Cross-Domain Representation Variance in Federated Prototype Learning with Heterogeneous Data Domains](https://mlsanity.com/paper/2403.09048/) (2024)
- [Efficient Differentially Private Secure Aggregation for Federated Learning via Hardness of Learning with Errors](https://mlsanity.com/paper/2112.06872/) (2021)
- [Computing Differential Privacy Guarantees for Heterogeneous Compositions Using FFT](https://mlsanity.com/paper/2102.12412/) (2021)
- [Distributed Differential Privacy in Multi-Armed Bandits](https://mlsanity.com/paper/2206.05772/) (2022)
- [Differentially Private Decoupled Graph Convolutions for Multigranular Topology Protection](https://mlsanity.com/paper/2307.06422/) (2023)
- [Leveraging Randomness in Model and Data Partitioning for Privacy Amplification](https://mlsanity.com/paper/2503.03043/) (2025)
- [Differentially Private Bayesian Neural Networks on Accuracy, Privacy and Reliability](https://mlsanity.com/paper/2107.08461/) (2021)
- [The Saddle-Point Accountant for Differential Privacy](https://mlsanity.com/paper/2208.09595/) (2022)
- [Backpropagation Clipping for Deep Learning with Differential Privacy](https://mlsanity.com/paper/2202.05089/) (2022)
- [DMM: Distributed Matrix Mechanism for Differentially-Private Federated Learning Based on Constant-Overhead Linear Secret Resharing](https://mlsanity.com/paper/2410.16161/) (2024)
- [Laplace Transform Interpretation of Differential Privacy](https://mlsanity.com/paper/2411.09142/) (2024)
- [The Poisson binomial mechanism for secure and private federated learning](https://mlsanity.com/paper/2207.09916/) (2022)
- [Towards Reliable and Generalizable Differentially Private Machine Learning (Extended Version)](https://mlsanity.com/paper/2508.15141/) (2025)

## Abstract (arXiv)

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.