### Poster

## Deletion Robust Submodular Maximization over Matroids

### PAUL DUETTING · Federico Fusco · Silvio Lattanzi · Ashkan Norouzi-Fard · Morteza Zadimoghaddam

##### Hall E #716

Keywords: [ OPT: Sampling and Optimization ] [ OPT: Discrete and Combinatorial Optimization ]

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 $O(k + \frac{d}{\eps^2}\log \frac{k}{\eps})$. In the streaming setting we provide a $(5.582+O(\varepsilon))$-approximation algorithm with summary size and memory $O(k + \frac{d}{\eps^2}\log \frac{k}{\eps})$. 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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