Deletion Robust Submodular Maximization over Matroids

• URL: http://arxiv.org/abs/2201.13128v1
• Date: Mon, 31 Jan 2022 11:15:56 GMT
• Title: Deletion Robust Submodular Maximization over Matroids
• Abstract summary: We study the deletion robust version of the problem under the classic matroids constraint. We present constant-factor approximation algorithms, whose space complexity depends on the rank $k$ of the matroid. We complement our theoretical results with an in-depth experimental analysis showing the effectiveness of our algorithms on real-world datasets.
• Score: 27.83996903538686
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Maximizing a monotone submodular function is a fundamental task in machine learning. In this paper, we study the deletion robust version of the problem under the classic matroids constraint. Here the goal is to extract a small size summary of the dataset that contains a high value independent set even after an adversary deleted some elements. We present constant-factor approximation algorithms, whose space complexity depends on the rank $k$ of the matroid and the number $d$ of deleted elements. In the centralized setting we present a $(3.582+O(\varepsilon))$-approximation algorithm with summary size $O(k + \frac{d \log k}{\varepsilon^2})$. In the streaming setting we provide a $(5.582+O(\varepsilon))$-approximation algorithm with summary size and memory $O(k + \frac{d \log k}{\varepsilon^2})$. We complement our theoretical results with an in-depth experimental analysis showing the effectiveness of our algorithms on real-world datasets.

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