# Beyond Adaptive Submodularity: Approximation Guarantees of Greedy Policy with Adaptive Submodularity Ratio

arXiv: https://arxiv.org/abs/1904.10748 · HTML: https://mlsanity.com/paper/1904.10748/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2019.

## Built on by (most cited first, 4 of 4)

- [Optimal Sampling Gaps for Adaptive Submodular Maximization](https://mlsanity.com/paper/2104.01750/) (2021)
- [Beyond Pointwise Submodularity: Non-Monotone Adaptive Submodular Maximization subject to Knapsack and k-System Constraints](https://mlsanity.com/paper/2104.04853/) (2021)
- [Partial-Monotone Adaptive Submodular Maximization](https://mlsanity.com/paper/2207.12840/) (2022)
- [Adaptive Combinatorial Maximization: Beyond Approximate Greedy Policies](https://mlsanity.com/paper/2404.01930/) (2024)

## Abstract (arXiv)

We propose a new concept named adaptive submodularity ratio to study the greedy policy for sequential decision making. While the greedy policy is known to perform well for a wide variety of adaptive stochastic optimization problems in practice, its theoretical properties have been analyzed only for a limited class of problems. We narrow the gap between theory and practice by using adaptive submodularity ratio, which enables us to prove approximation guarantees of the greedy policy for a substantially wider class of problems. Examples of newly analyzed problems include important applications such as adaptive influence maximization and adaptive feature selection. Our adaptive submodularity ratio also provides bounds of adaptivity gaps. Experiments confirm that the greedy policy performs well with the applications being considered compared to standard heuristics.