Toward Highly Efficient and Private Submodular Maximization via Matrix-Based Acceleration

Boyu Liu; Lianke Qin; Zhao Song; Yitan Wang; Jiale Zhao

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arXiv · 2305.08367

Toward Highly Efficient and Private Submodular Maximization via Matrix-Based Acceleration

Boyu Liu·Lianke Qin·Zhao Song·Yitan Wang·Jiale Zhao

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Abstract

Submodular function maximization is a critical building block for diverse tasks, such as document summarization, sensor placement, and image segmentation. Yet its practical utility is often limit by the $O(knd^2)$ computational bottleneck. In this paper, we propose an integrated framework that addresses efficiency and privacy simultaneously. First, we introduce a novel matrix-based computation paradigm that accelerates function evaluations. Second, we develop approximate data structures that further streamline the optimization process, achieving a theoretical complexity of $O(\epsilon^{-2}(nd+kn+kd^2)\log(k/\delta))$. Third, we integrate ($\epsilon, \delta$)-DP guaranties to address the privacy concerns inherent in sensitive optimization tasks.

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Boyu Liu, Lianke Qin, Zhao Song, Yitan Wang, Jiale Zhao. 2023-05-15. Toward Highly Efficient and Private Submodular Maximization via Matrix-Based Acceleration. https://arxiv.org/abs/2305.08367

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