# Robust Maximization of Non-Submodular Objectives

arXiv: https://arxiv.org/abs/1802.07073 · HTML: https://mlsanity.com/paper/1802.07073/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2018.

## Built on by (most cited first, 7 of 7)

- [Minimax Optimization: The Case of Convex-Submodular](https://mlsanity.com/paper/2111.01262/) (2021)
- [Maximum n-times Coverage for Vaccine Design](https://mlsanity.com/paper/2101.10902/) (2021)
- [Online Nonsubmodular Minimization with Delayed Costs: From Full Information to Bandit Feedback](https://mlsanity.com/paper/2205.07217/) (2022)
- [Parallel Quasi-concave set optimization: A new frontier that scales without needing submodularity](https://mlsanity.com/paper/2108.08758/) (2021)
- [Online Subset Selection using α-Core with no Augmented Regret](https://mlsanity.com/paper/2209.14222/) (2022)
- [Supermodular Rank: Set Function Decomposition and Optimization](https://mlsanity.com/paper/2305.14632/) (2023)
- [Robust Information Selection for Hypothesis Testing with Misclassification Penalties](https://mlsanity.com/paper/2502.14738/) (2025)

## Abstract (arXiv)

We study the problem of maximizing a monotone set function subject to a cardinality constraint k in the setting where some number of elements τ is deleted from the returned set. The focus of this work is on the worst-case adversarial setting. While there exist constant-factor guarantees when the function is submodular, there are no guarantees for non-submodular objectives. In this work, we present a new algorithm Oblivious-Greedy and prove the first constant-factor approximation guarantees for a wider class of non-submodular objectives. The obtained theoretical bounds are the first constant-factor bounds that also hold in the linear regime, i.e. when the number of deletions τ is linear in k. Our bounds depend on established parameters such as the submodularity ratio and some novel ones such as the inverse curvature. We bound these parameters for two important objectives including support selection and variance reduction. Finally, we numerically demonstrate the robust performance of Oblivious-Greedy for these two objectives on various datasets.