Multi-Objective Submodular Maximization with Differential Privacy

2026-06-03

AI Summary

This work addresses the problem of cardinality-constrained multi-objective submodular maximization under differential privacy, where the goal is to select at most $k$ elements from sensitive data to maximize the minimum of $d$ monotone submodular functions. The study introduces differential privacy into this setting for the first time and proposes two novel algorithms: one extends the classical greedy strategy with privacy guarantees, and the other integrates a function truncation technique. Both algorithms provide rigorous theoretical approximation guarantees. Empirical evaluations on maximum coverage and facility location tasks demonstrate that the proposed methods effectively balance utility and privacy, thereby bridging a critical gap in the intersection of differential privacy and multi-objective submodular optimization.

Abstract

In this paper, we study multi-objective submodular maximization (MOSM) subject to a cardinality constraint under differential privacy (DP). Specifically, we aim to select a set of at most $k \in \mathbb{Z}_{+}$ elements to maximize the minimum of $d > 1$ monotone submodular functions while satisfying $\varepsilon$-DP. Although extensive studies have been conducted on both differentially private single-objective submodular maximization on sensitive data and non-private MOSM, to the best of our knowledge, there has not yet been any prior work on MOSM with DP. We propose two novel algorithms: the first extends the classic greedy algorithm and the second employs a truncation technique, both of which are integrated with DP mechanisms for privacy protection and achieve approximation guarantees for MOSM. Finally, we conduct numerical experiments on two submodular maximization applications, namely maximum coverage and facility location, in multi-objective settings to validate the efficacy and efficiency of our proposed algorithms.

Problem

• multi-objective submodular maximization
• differential privacy
• cardinality constraint
• monotone submodular functions

Innovation

• Multi-Objective Submodular Maximization
• Differential Privacy
• Greedy Algorithm
• Truncation Technique
• Approximation Guarantee