Differentially Private Multi-objective Selection: Pareto and Aggregation Approaches

TL;DR

This paper introduces two new differentially private mechanisms, PrivPareto and PrivAgg, for multi-objective optimization, demonstrating improved utility in real-world applications like decision trees and social network analysis.

Contribution

The paper presents novel privacy-preserving mechanisms for multi-objective selection, supporting both Pareto and aggregation approaches with theoretical sensitivity analysis.

Findings

Local sensitivity approaches outperform global sensitivity in utility.

Methods perform well with privacy budgets in [0.01, 1].

Applicable to cost-sensitive decision trees and social network influence.

Abstract

Differentially private selection mechanisms are fundamental building blocks for privacy-preserving data analysis. While numerous mechanisms exist for single-objective selection, many real-world applications require optimizing multiple competing objectives simultaneously. We present two novel mechanisms for differentially private multi-objective selection: PrivPareto and PrivAgg. PrivPareto uses a novel Pareto score to identify solutions near the Pareto frontier, while PrivAgg enables privacy-preserving weighted aggregation of multiple objectives. Both mechanisms support global and local sensitivity approaches, with comprehensive theoretical analysis showing how to compose sensitivities of multiple utility functions. We demonstrate the practical applicability through two real-world applications: cost-sensitive decision tree construction and multi-objective influential node selection in social networks. The experimental results showed that our local sensitivity-based approaches achieve significantly better utility compared to global sensitivity approaches across both applications and both Pareto and Aggregation approaches. Moreover, the local sensitivity-based approaches are able to perform well with typical privacy budget values $\epsilon \in [0.01, 1]$ in most experiments.