# Learning to Act Greedily: Polymatroid Semi-Bandits

arXiv: https://arxiv.org/abs/1405.7752 · HTML: https://mlsanity.com/paper/1405.7752/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2014.

## Built on by (most cited first, 2 of 2)

- [Matroid Semi-Bandits in Sublinear Time](https://mlsanity.com/paper/2405.17968/) (2024)
- [Bandits on graphs and structures](https://mlsanity.com/paper/2605.03493/) (2026)

## Abstract (arXiv)

Many important optimization problems, such as the minimum spanning tree and minimum-cost flow, can be solved optimally by a greedy method. In this work, we study a learning variant of these problems, where the model of the problem is unknown and has to be learned by interacting repeatedly with the environment in the bandit setting. We formalize our learning problem quite generally, as learning how to maximize an unknown modular function on a known polymatroid. We propose a computationally efficient algorithm for solving our problem and bound its expected cumulative regret. Our gap-dependent upper bound is tight up to a constant and our gap-free upper bound is tight up to polylogarithmic factors. Finally, we evaluate our method on three problems and demonstrate that it is practical.