# Differential Privacy via Distributionally Robust Optimization

arXiv: https://arxiv.org/abs/2304.12681 · HTML: https://mlsanity.com/paper/2304.12681/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 71 references that are in the map.
- First posted on arXiv 25 Apr 2023.

## Builds on (most cited first, 21 of 21)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018)
- [Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning](https://mlsanity.com/paper/1908.08729/) (2019)
- [Adding Gradient Noise Improves Learning for Very Deep Networks](https://mlsanity.com/paper/1511.06807/) (2015)
- [Concentrated Differential Privacy](https://mlsanity.com/paper/1603.01887/) (2016)
- [The Discrete Gaussian for Differential Privacy](https://mlsanity.com/paper/2004.00010/) (2020)
- [SoK: Differential Privacies](https://mlsanity.com/paper/1906.01337/) (2019)
- [Near Instance-Optimality in Differential Privacy](https://mlsanity.com/paper/2005.10630/) (2020)
- [Privacy-Preserving Dynamic Personalized Pricing with Demand Learning](https://mlsanity.com/paper/2009.12920/) (2020)
- [Differential Privacy in Personalized Pricing with Nonparametric Demand Models](https://mlsanity.com/paper/2109.04615/) (2021)
- [Differentially Private Distributed Constrained Optimization](https://mlsanity.com/paper/1411.4105/) (2014)
- [Reviewing and Improving the Gaussian Mechanism for Differential Privacy](https://mlsanity.com/paper/1911.12060/) (2019)
- [Differentially Private Coordinate Descent for Composite Empirical Risk Minimization](https://mlsanity.com/paper/2110.11688/) (2021)
- [Optimal Noise-Adding Mechanism in Additive Differential Privacy](https://mlsanity.com/paper/1809.10224/) (2018)
- [Privately Solving Linear Programs](https://mlsanity.com/paper/1402.3631/) (2014)
- [A Members First Approach to Enabling LinkedIn's Labor Market Insights at Scale](https://mlsanity.com/paper/2010.13981/) (2020)
- [U.S. Broadband Coverage Data Set: A Differentially Private Data Release](https://mlsanity.com/paper/2103.14035/) (2021)
- [Google COVID-19 Vaccination Search Insights: Anonymization Process Description](https://mlsanity.com/paper/2107.01179/) (2021)
- [Jointly Private Convex Programming](https://mlsanity.com/paper/1411.0998/) (2014)
- [Convex Optimal Uncertainty Quantification](https://mlsanity.com/paper/1311.7130/) (2013)
- [Privacy Preserving Linear Programming](https://mlsanity.com/paper/1610.02339/) (2016)

## Built on by (most cited first, 2 of 2)

- [Assured autonomy: How operations research powers and orchestrates generative AI systems](https://mlsanity.com/paper/2512.23978/) (2025)
- [Differentially Private Non-convex Distributionally Robust Optimization](https://mlsanity.com/paper/2602.16155/) (2026)

## Abstract (arXiv)

In recent years, differential privacy has emerged as the de facto standard for sharing statistics of datasets while limiting the disclosure of private information about the involved individuals. This is achieved by randomly perturbing the statistics to be published, which in turn leads to a privacy-accuracy trade-off: larger perturbations provide stronger privacy guarantees, but they result in less accurate statistics that offer lower utility to the recipients. Of particular interest are therefore optimal mechanisms that provide the highest accuracy for a pre-selected level of privacy. To date, work in this area has focused on specifying families of perturbations a priori and subsequently proving their asymptotic and/or best-in-class optimality. In this paper, we develop a class of mechanisms that enjoy non-asymptotic and unconditional optimality guarantees. To this end, we formulate the mechanism design problem as an infinite-dimensional distributionally robust optimization problem. We show that the problem affords a strong dual, and we exploit this duality to develop converging hierarchies of finite-dimensional upper and lower bounding problems. Our upper (primal) bounds correspond to implementable perturbations whose suboptimality can be bounded by our lower (dual) bounds. Both bounding problems can be solved within seconds via cutting plane techniques that exploit the inherent problem structure. Our numerical experiments demonstrate that our perturbations can outperform the previously best results from the literature on artificial as well as standard benchmark problems.