# Submodular Reinforcement Learning

arXiv: https://arxiv.org/abs/2307.13372 · HTML: https://mlsanity.com/paper/2307.13372/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 57 references that are in the map.
- First posted on arXiv 25 Jul 2023.

## Builds on (most cited first, 28 of 28)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Provably Efficient Maximum Entropy Exploration](https://mlsanity.com/paper/1812.02690/) (2018)
- [Global Optimality Guarantees For Policy Gradient Methods](https://mlsanity.com/paper/1906.01786/) (2019)
- [Reward is enough for convex MDPs](https://mlsanity.com/paper/2106.00661/) (2021)
- [On the Expressivity of Markov Reward](https://mlsanity.com/paper/2111.00876/) (2021)
- [Optimization-Based Autonomous Racing of 1:43 Scale RC Cars](https://mlsanity.com/paper/1711.07300/) (2017)
- [Submodularity In Machine Learning and Artificial Intelligence](https://mlsanity.com/paper/2202.00132/) (2022)
- [Guarantees for Greedy Maximization of Non-submodular Functions with Applications](https://mlsanity.com/paper/1703.02100/) (2017)
- [Gradient Methods for Submodular Maximization](https://mlsanity.com/paper/1708.03949/) (2017)
- [On the Theory of Reinforcement Learning with Once-per-Episode Feedback](https://mlsanity.com/paper/2105.14363/) (2021)
- [Guaranteed Non-convex Optimization: Submodular Maximization over Continuous Domains](https://mlsanity.com/paper/1606.05615/) (2016)
- [Challenging Common Assumptions in Convex Reinforcement Learning](https://mlsanity.com/paper/2202.01511/) (2022)
- [Active Exploration in Markov Decision Processes](https://mlsanity.com/paper/1902.11199/) (2019)
- [Blocking Bandits](https://mlsanity.com/paper/1907.11975/) (2019)
- [Continuous DR-submodular Maximization: Structure and Algorithms](https://mlsanity.com/paper/1711.02515/) (2017)
- [Information Directed Reward Learning for Reinforcement Learning](https://mlsanity.com/paper/2102.12466/) (2021)
- [Active Model Estimation in Markov Decision Processes](https://mlsanity.com/paper/2003.03297/) (2020)
- [Active Exploration via Experiment Design in Markov Chains](https://mlsanity.com/paper/2206.14332/) (2022)
- [Inverse Reinforcement Learning in Contextual MDPs](https://mlsanity.com/paper/1905.09710/) (2019)
- [Submodularity in Action: From Machine Learning to Signal Processing Applications](https://mlsanity.com/paper/2006.09905/) (2020)
- [Stochastic Submodular Maximization: The Case of Coverage Functions](https://mlsanity.com/paper/1711.01566/) (2017)
- [Near-Optimal Multi-Agent Learning for Safe Coverage Control](https://mlsanity.com/paper/2210.06380/) (2022)
- [Fast Semidifferential-based Submodular Function Optimization](https://mlsanity.com/paper/1308.1006/) (2013)
- [Competitive Policy Optimization](https://mlsanity.com/paper/2006.10611/) (2020)
- [Planning with Submodular Objective Functions](https://mlsanity.com/paper/2010.11863/) (2020)
- [Sensing Cox Processes via Posterior Sampling and Positive Bases](https://mlsanity.com/paper/2110.11181/) (2021)

## Built on by (most cited first, 23 of 23)

- [MaxInfoRL: Boosting exploration in reinforcement learning through information gain maximization](https://mlsanity.com/paper/2412.12098/) (2024)
- [Flow Density Control: Generative Optimization Beyond Entropy-Regularized Fine-Tuning](https://mlsanity.com/paper/2511.22640/) (2025)
- [Global Reinforcement Learning: Beyond Linear and Convex Rewards via Submodular Semi-gradient Methods](https://mlsanity.com/paper/2407.09905/) (2024)
- [Provable Maximum Entropy Manifold Exploration via Diffusion Models](https://mlsanity.com/paper/2506.15385/) (2025)
- [Safe Guaranteed Exploration for Non-linear Systems](https://mlsanity.com/paper/2402.06562/) (2024)
- [Efficient Tail-Aware Generative Optimization via Flow Model Fine-Tuning](https://mlsanity.com/paper/2602.16796/) (2026)
- [Verifier-Constrained Flow Expansion for Discovery Beyond the Data](https://mlsanity.com/paper/2602.15984/) (2026)
- [Global Rewards in Restless Multi-Armed Bandits](https://mlsanity.com/paper/2406.00738/) (2024)
- [On the Global Optimality of Policy Gradient Methods in General Utility Reinforcement Learning](https://mlsanity.com/paper/2410.04108/) (2024)
- [Performance-driven Constrained Optimal Auto-Tuner for MPC](https://mlsanity.com/paper/2503.07127/) (2025)
- [Finite-Sample-Based Reachability for Safe Control with Gaussian Process Dynamics](https://mlsanity.com/paper/2505.07594/) (2025)
- [Reinforcement Learning from Human Feedback without Reward Inference: Model-Free Algorithm and Instance-Dependent Analysis](https://mlsanity.com/paper/2406.07455/) (2024)
- [Efficient Reinforcement Learning in Probabilistic Reward Machines](https://mlsanity.com/paper/2408.10381/) (2024)
- [A State Representation for Diminishing Rewards](https://mlsanity.com/paper/2309.03710/) (2023)
- [SMART: Self-learning Meta-strategy Agent for Reasoning Tasks](https://mlsanity.com/paper/2410.16128/) (2024)
- [Convex Markov Games: A New Frontier for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2410.16600/) (2024)
- [Synergistic Reinforcement and Imitation Learning for Vision-driven Autonomous Flight of UAV Along River](https://mlsanity.com/paper/2401.09332/) (2024)
- [Deep Submodular Peripteral Networks](https://mlsanity.com/paper/2403.08199/) (2024)
- [Safe and Near-Optimal Control with Online Dynamics Learning](https://mlsanity.com/paper/2509.16650/) (2025)
- [Scalable Submodular Policy Optimization via Pruned Submodularity Graph](https://mlsanity.com/paper/2507.13834/) (2025)
- [Fast Approximation Algorithm for Non-Monotone DR-submodular Maximization under Size Constraint](https://mlsanity.com/paper/2511.02254/) (2025)
- [Global Optimality for Constrained Exploration via Penalty Regularization](https://mlsanity.com/paper/2604.28144/) (2026)
- [Strong and Compact Policies for Submodular Markov Decision Processes via LP-Based Submodular Orienteering](https://mlsanity.com/paper/2609.15539/) (2026)

## Abstract (arXiv)

In reinforcement learning (RL), rewards of states are typically considered additive, and following the Markov assumption, they are textitindependent of states visited previously. In many important applications, such as coverage control, experiment design and informative path planning, rewards naturally have diminishing returns, i.e., their value decreases in light of similar states visited previously. To tackle this, we propose textitsubmodular RL (SubRL), a paradigm which seeks to optimize more general, non-additive (and history-dependent) rewards modelled via submodular set functions which capture diminishing returns. Unfortunately, in general, even in tabular settings, we show that the resulting optimization problem is hard to approximate. On the other hand, motivated by the success of greedy algorithms in classical submodular optimization, we propose SubPO, a simple policy gradient-based algorithm for SubRL that handles non-additive rewards by greedily maximizing marginal gains. Indeed, under some assumptions on the underlying Markov Decision Process (MDP), SubPO recovers optimal constant factor approximations of submodular bandits. Moreover, we derive a natural policy gradient approach for locally optimizing SubRL instances even in large state- and action- spaces. We showcase the versatility of our approach by applying SubPO to several applications, such as biodiversity monitoring, Bayesian experiment design, informative path planning, and coverage maximization. Our results demonstrate sample efficiency, as well as scalability to high-dimensional state-action spaces.