Differentially Private Algorithms for Linear Queries via Stochastic Convex Optimization

TL;DR

This paper introduces new differentially private algorithms for answering linear queries by formulating the problem as a saddle-point optimization, improving accuracy evaluation with respect to the true data distribution.

Contribution

It presents two novel algorithms based on stochastic convex optimization and Frank-Wolfe methods for differential privacy, with a focus on true data distribution accuracy.

Findings

Algorithms achieve differential privacy guarantees.

Enhanced accuracy evaluation methodology.

Applicable to finite linear query sets.

Abstract

This article establishes a method to answer a finite set of linear queries on a given dataset while ensuring differential privacy. To achieve this, we formulate the corresponding task as a saddle-point problem, i.e. an optimization problem whose solution corresponds to a distribution minimizing the difference between answers to the linear queries based on the true distribution and answers from a differentially private distribution. Against this background, we establish two new algorithms for corresponding differentially private data release: the first is based on the differentially private Frank-Wolfe method, the second combines randomized smoothing with stochastic convex optimization techniques for a solution to the saddle-point problem. While previous works assess the accuracy of differentially private algorithms with reference to the empirical data distribution, a key contribution of our work is a more natural evaluation of the proposed algorithms' accuracy with reference to the true data-generating distribution.