# Convex Optimization for Linear Query Processing under Approximate Differential Privacy

arXiv: https://arxiv.org/abs/1602.04302 · HTML: https://mlsanity.com/paper/1602.04302/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2016.

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

- [(Amplified) Banded Matrix Factorization: A unified approach to private training](https://mlsanity.com/paper/2306.08153/) (2023)
- [Gradient Descent with Linearly Correlated Noise: Theory and Applications to Differential Privacy](https://mlsanity.com/paper/2302.01463/) (2023)
- [Answering Private Linear Queries Adaptively using the Common Mechanism](https://mlsanity.com/paper/2212.00135/) (2022)
- [ResidualPlanner+: a scalable matrix mechanism for marginals and beyond](https://mlsanity.com/paper/2305.08175/) (2023)
- [Accurate and Scalable Matrix Mechanisms via Divide and Conquer](https://mlsanity.com/paper/2604.00868/) (2026)

## Abstract (arXiv)

Differential privacy enables organizations to collect accurate aggregates over sensitive data with strong, rigorous guarantees on individuals' privacy. Previous work has found that under differential privacy, computing multiple correlated aggregates as a batch, using an appropriate strategy, may yield higher accuracy than computing each of them independently. However, finding the best strategy that maximizes result accuracy is non-trivial, as it involves solving a complex constrained optimization program that appears to be non-linear and non-convex. Hence, in the past much effort has been devoted in solving this non-convex optimization program. Existing approaches include various sophisticated heuristics and expensive numerical solutions. None of them, however, guarantees to find the optimal solution of this optimization problem. This paper points out that under (ε, δ)-differential privacy, the optimal solution of the above constrained optimization problem in search of a suitable strategy can be found, rather surprisingly, by solving a simple and elegant convex optimization program. Then, we propose an efficient algorithm based on Newton's method, which we prove to always converge to the optimal solution with linear global convergence rate and quadratic local convergence rate. Empirical evaluations demonstrate the accuracy and efficiency of the proposed solution.