# Submodular Maximization with Limited Function Access

arXiv: https://arxiv.org/abs/2201.00724 · HTML: https://mlsanity.com/paper/2201.00724/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jan 2022.

## Built on by (most cited first, 3 of 3)

- [Resource-Aware Distributed Submodular Maximization: A Paradigm for Multi-Robot Decision-Making](https://mlsanity.com/paper/2204.07520/) (2022)
- [Online Submodular Coordination with Bounded Tracking Regret: Theory, Algorithm, and Applications to Multi-Robot Coordination](https://mlsanity.com/paper/2209.12429/) (2022)
- [Communication- and Computation-Efficient Distributed Submodular Optimization in Robot Mesh Networks](https://mlsanity.com/paper/2407.10382/) (2024)

## Abstract (arXiv)

We consider a class of submodular maximization problems in which decision-makers have limited access to the objective function. We explore scenarios where the decision-maker can observe only pairwise information, i.e., can evaluate the objective function on sets of size two. We begin with a negative result that no algorithm using only k-wise information can guarantee performance better than k/n. We present two algorithms that utilize only pairwise information about the function and characterize their performance relative to the optimal, which depends on the curvature of the submodular function. Additionally, if the submodular function possess a property called supermodularity of conditioning, then we can provide a method to bound the performance based purely on pairwise information. The proposed algorithms offer significant computational speedups over a traditional greedy strategy. A by-product of our study is the introduction of two new notions of curvature, the k-Marginal Curvature and the k-Cardinality Curvature. Finally, we present experiments highlighting the performance of our proposed algorithms in terms of approximation and time complexity.