# Planning with Submodular Objective Functions

arXiv: https://arxiv.org/abs/2010.11863 · HTML: https://mlsanity.com/paper/2010.11863/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2020.

## Built on by (most cited first, 5 of 5)

- [Submodular Reinforcement Learning](https://mlsanity.com/paper/2307.13372/) (2023)
- [Global Reinforcement Learning: Beyond Linear and Convex Rewards via Submodular Semi-gradient Methods](https://mlsanity.com/paper/2407.09905/) (2024)
- [A State Representation for Diminishing Rewards](https://mlsanity.com/paper/2309.03710/) (2023)
- [When Does Trajectory-Level Supervision Permit Efficient Offline Reinforcement Learning?](https://mlsanity.com/paper/2606.18531/) (2026)
- [Strong and Compact Policies for Submodular Markov Decision Processes via LP-Based Submodular Orienteering](https://mlsanity.com/paper/2609.15539/) (2026)

## Abstract (arXiv)

We study planning with submodular objective functions, where instead of maximizing the cumulative reward, the goal is to maximize the objective value induced by a submodular function. Our framework subsumes standard planning and submodular maximization with cardinality constraints as special cases, and thus many practical applications can be naturally formulated within our framework. Based on the notion of multilinear extension, we propose a novel and theoretically principled algorithmic framework for planning with submodular objective functions, which recovers classical algorithms when applied to the two special cases mentioned above. Empirically, our approach significantly outperforms baseline algorithms on synthetic environments and navigation tasks.