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arXiv · 2606.14951

Differentially Private Submodular Maximization with a Knapsack Constraint

Ron Zadicario·Tova Milo
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Abstract

Submodular maximization subject to a knapsack constraint (SMK) is a fundamental problem in discrete optimization, with wide-ranging applications in machine learning and related fields. As these applications increasingly involve sensitive individual data, there is a growing need for high-utility algorithms that provide formal privacy guarantees. In this work, we study the SMK problem under differential privacy, considering both monotone and non-monotone objective functions. For monotone objectives, we propose a differentially private algorithm that achieves the optimal $(1-1/e)$-approximation ratio while significantly improving both additive error and query complexity over prior work. We also present a more efficient algorithm for the same setting, achieving a $1/2$-approximation. For non-monotone objectives, we introduce, to our knowledge, the first differentially private algorithm with provable guarantees, achieving a $1/4$-approximation in expectation and an additive error comparable to the best known for monotone objective functions.

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Ron Zadicario, Tova Milo. 2026-06-12. Differentially Private Submodular Maximization with a Knapsack Constraint. https://arxiv.org/abs/2606.14951

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