# Submodular Optimization under Noise

arXiv: https://arxiv.org/abs/1601.03095 · HTML: https://mlsanity.com/paper/1601.03095/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jan 2016.

## Built on by (most cited first, 11 of 11)

- [Training Data Subset Selection for Regression with Controlled Generalization Error](https://mlsanity.com/paper/2106.12491/) (2021)
- [Maximizing approximately k-submodular functions](https://mlsanity.com/paper/2101.07157/) (2021)
- [Accelerating Matroid Optimization through Fast Imprecise Oracles](https://mlsanity.com/paper/2402.02774/) (2024)
- [Instance Specific Approximations for Submodular Maximization](https://mlsanity.com/paper/2102.11911/) (2021)
- [Linear Submodular Maximization with Bandit Feedback](https://mlsanity.com/paper/2407.02601/) (2024)
- [A Unified Approach to Submodular Maximization Under Noise](https://mlsanity.com/paper/2510.21128/) (2025)
- [CM-EVS: Sparse Panoramic RGB-D-Pose Data for Complete Scene Coverage](https://mlsanity.com/paper/2605.15597/) (2026)
- [Logarithmic Regret for Unconstrained Submodular Maximization Stochastic Bandit](https://mlsanity.com/paper/2410.08578/) (2024)
- [Multi-Agent Reinforcement Learning with Submodular Reward](https://mlsanity.com/paper/2603.06810/) (2026)
- [Stochastic Sequential Search in Very-High-Dimensional Feature Selection](https://mlsanity.com/paper/2608.01502/) (2026)
- [Adversarial Resilience of Poisson-Process Submodular Maximization over Matroids, and Full-Bandit Learning](https://mlsanity.com/paper/2608.12134/) (2026)

## Abstract (arXiv)

We consider the problem of maximizing a monotone submodular function under noise. There has been a great deal of work on optimization of submodular functions under various constraints, resulting in algorithms that provide desirable approximation guarantees. In many applications, however, we do not have access to the submodular function we aim to optimize, but rather to some erroneous or noisy version of it. This raises the question of whether provable guarantees are obtainable in presence of error and noise. We provide initial answers, by focusing on the question of maximizing a monotone submodular function under a cardinality constraint when given access to a noisy oracle of the function. We show that: - For a cardinality constraint k ≥ 2, there is an approximation algorithm whose approximation ratio is arbitrarily close to 1-1/e; - For k=1 there is an algorithm whose approximation ratio is arbitrarily close to 1/2. No randomized algorithm can obtain an approximation ratio better than 1/2+o(1); -If the noise is adversarial, no non-trivial approximation guarantee can be obtained.