# The Saddle-Point Accountant for Differential Privacy

arXiv: https://arxiv.org/abs/2208.09595 · HTML: https://mlsanity.com/paper/2208.09595/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 43 references that are in the map.
- First posted on arXiv 20 Aug 2022.

## Builds on (most cited first, 17 of 17)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [The Composition Theorem for Differential Privacy](https://mlsanity.com/paper/1311.0776/) (2013)
- [Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergences](https://mlsanity.com/paper/1807.01647/) (2018)
- [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018)
- [R'enyi Differential Privacy of the Sampled Gaussian Mechanism](https://mlsanity.com/paper/1908.10530/) (2019)
- [Numerical Composition of Differential Privacy](https://mlsanity.com/paper/2106.02848/) (2021)
- [The Discrete Gaussian for Differential Privacy](https://mlsanity.com/paper/2004.00010/) (2020)
- [Optimal Accounting of Differential Privacy via Characteristic Function](https://mlsanity.com/paper/2106.08567/) (2021)
- [Hypothesis Testing Interpretations and Renyi Differential Privacy](https://mlsanity.com/paper/1905.09982/) (2019)
- [Connect the Dots: Tighter Discrete Approximations of Privacy Loss Distributions](https://mlsanity.com/paper/2207.04380/) (2022)
- [Tight Differential Privacy for Discrete-Valued Mechanisms and for the Subsampled Gaussian Mechanism Using FFT](https://mlsanity.com/paper/2006.07134/) (2020)
- [A Better Bound Gives a Hundred Rounds: Enhanced Privacy Guarantees via f-Divergences](https://mlsanity.com/paper/2001.05990/) (2020)
- [Computing Differential Privacy Guarantees for Heterogeneous Compositions Using FFT](https://mlsanity.com/paper/2102.12412/) (2021)
- [R'enyi Differential Privacy Mechanisms for Posterior Sampling](https://mlsanity.com/paper/1710.00892/) (2017)
- [Faster Privacy Accounting via Evolving Discretization](https://mlsanity.com/paper/2207.04381/) (2022)
- [Edgeworth Accountant: An Analytical Approach to Differential Privacy Composition](https://mlsanity.com/paper/2206.04236/) (2022)

## Built on by (most cited first, 5 of 5)

- [Composition of Differential Privacy & Privacy Amplification by Subsampling](https://mlsanity.com/paper/2210.00597/) (2022)
- [Bounding data reconstruction attacks with the hypothesis testing interpretation of differential privacy](https://mlsanity.com/paper/2307.03928/) (2023)
- [Unifying Re-Identification, Attribute Inference, and Data Reconstruction Risks in Differential Privacy](https://mlsanity.com/paper/2507.06969/) (2025)
- [A Randomized Approach for Tight Privacy Accounting](https://mlsanity.com/paper/2304.07927/) (2023)
- [Attack-Aware Noise Calibration for Differential Privacy](https://mlsanity.com/paper/2407.02191/) (2024)

## Abstract (arXiv)

We introduce a new differential privacy (DP) accountant called the saddle-point accountant (SPA). SPA approximates privacy guarantees for the composition of DP mechanisms in an accurate and fast manner. Our approach is inspired by the saddle-point method -- a ubiquitous numerical technique in statistics. We prove rigorous performance guarantees by deriving upper and lower bounds for the approximation error offered by SPA. The crux of SPA is a combination of large-deviation methods with central limit theorems, which we derive via exponentially tilting the privacy loss random variables corresponding to the DP mechanisms. One key advantage of SPA is that it runs in constant time for the n-fold composition of a privacy mechanism. Numerical experiments demonstrate that SPA achieves comparable accuracy to state-of-the-art accounting methods with a faster runtime.