# Privacy Amplification of Iterative Algorithms via Contraction Coefficients

arXiv: https://arxiv.org/abs/2001.06546 · HTML: https://mlsanity.com/paper/2001.06546/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2020.

## Built on by (most cited first, 7 of 7)

- [Differential Privacy Dynamics of Langevin Diffusion and Noisy Gradient Descent](https://mlsanity.com/paper/2102.05855/) (2021)
- [Faster high-accuracy log-concave sampling via algorithmic warm starts](https://mlsanity.com/paper/2302.10249/) (2023)
- [Resolving the Mixing Time of the Langevin Algorithm to its Stationary Distribution for Log-Concave Sampling](https://mlsanity.com/paper/2210.08448/) (2022)
- [Generalization Bounds for Noisy Iterative Algorithms Using Properties of Additive Noise Channels](https://mlsanity.com/paper/2102.02976/) (2021)
- [Privacy Loss of Noisy Stochastic Gradient Descent Might Converge Even for Non-Convex Losses](https://mlsanity.com/paper/2305.09903/) (2023)
- [Privacy Amplification via Iteration for Shuffled and Online PNSGD](https://mlsanity.com/paper/2106.11767/) (2021)
- [Convex Approximation of Two-Layer ReLU Networks for Hidden State Differential Privacy](https://mlsanity.com/paper/2407.04884/) (2024)

## Abstract (arXiv)

We investigate the framework of privacy amplification by iteration, recently proposed by Feldman et al., from an information-theoretic lens. We demonstrate that differential privacy guarantees of iterative mappings can be determined by a direct application of contraction coefficients derived from strong data processing inequalities for f-divergences. In particular, by generalizing the Dobrushin's contraction coefficient for total variation distance to an f-divergence known as Eγ-divergence, we derive tighter bounds on the differential privacy parameters of the projected noisy stochastic gradient descent algorithm with hidden intermediate updates.