Robust Optimization for Local Differential Privacy

TL;DR

This paper introduces a robust optimization framework for local differential privacy, ensuring data privacy across uncertain data distributions by formulating and solving a convex optimization problem with closed-form solutions.

Contribution

It formulates the problem of data release under local differential privacy as a robust convex optimization, providing closed-form solutions and analyzing different robustness scenarios.

Findings

Derived closed-form expressions for dual constraints.

Formulated convex optimization problems for different robustness settings.

Compared performance of multiple optimization approaches.

Abstract

We consider the setting of publishing data without leaking sensitive information. We do so in the framework of Robust Local Differential Privacy (RLDP). This ensures privacy for all distributions of the data in an uncertainty set. We formulate the problem of finding the optimal data release protocol as a robust optimization problem. By deriving closed-form expressions for the duals of the constraints involved we obtain a convex optimization problem. We compare the performance of four possible optimization problems depending on whether or not we require robustness in i) utility and ii) privacy.