# Online Submodular Maximization under a Matroid Constraint with Application to Learning Assignments

arXiv: https://arxiv.org/abs/1407.1082 · HTML: https://mlsanity.com/paper/1407.1082/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2014.

## Built on by (most cited first, 17 of 17)

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- [Improved Regret Bounds for Online Submodular Maximization](https://mlsanity.com/paper/2106.07836/) (2021)
- [No-Regret Mnatural-Concave Function Maximization: Stochastic Bandit Algorithms and Hardness of Adversarial Full-Information Setting](https://mlsanity.com/paper/2405.12439/) (2024)
- [Select Smarter, Not More: Prompt-Aware Evaluation Scheduling with Submodular Guarantees](https://mlsanity.com/paper/2604.11328/) (2026)
- [Scalable Projection-Free Optimization](https://mlsanity.com/paper/2105.03527/) (2021)
- [Online Subset Selection using α-Core with no Augmented Regret](https://mlsanity.com/paper/2209.14222/) (2022)
- [High Probability Bounds for Stochastic Continuous Submodular Maximization](https://mlsanity.com/paper/2303.11937/) (2023)
- [Leveraging Untrustworthy Commands for Multi-Robot Coordination in Unpredictable Environments: A Bandit Submodular Maximization Approach](https://mlsanity.com/paper/2309.16161/) (2023)
- [Logarithmic Regret for Unconstrained Submodular Maximization Stochastic Bandit](https://mlsanity.com/paper/2410.08578/) (2024)
- [Learning to Sparsify Stochastic Linear Bandits](https://mlsanity.com/paper/2605.10151/) (2026)
- [Distributed Online Bandit Submodular Maximization with Bounded Sampling Violations](https://mlsanity.com/paper/2607.00680/) (2026)

## Abstract (arXiv)

Which ads should we display in sponsored search in order to maximize our revenue? How should we dynamically rank information sources to maximize the value of the ranking? These applications exhibit strong diminishing returns: Redundancy decreases the marginal utility of each ad or information source. We show that these and other problems can be formalized as repeatedly selecting an assignment of items to positions to maximize a sequence of monotone submodular functions that arrive one by one. We present an efficient algorithm for this general problem and analyze it in the no-regret model. Our algorithm possesses strong theoretical guarantees, such as a performance ratio that converges to the optimal constant of 1 - 1/e. We empirically evaluate our algorithm on two real-world online optimization problems on the web: ad allocation with submodular utilities, and dynamically ranking blogs to detect information cascades. Finally, we present a second algorithm that handles the more general case in which the feasible sets are given by a matroid constraint, while still maintaining a 1 - 1/e asymptotic performance ratio.