# Greedy based Value Representation for Optimal Coordination in Multi-agent Reinforcement Learning

arXiv: https://arxiv.org/abs/2211.12075 · HTML: https://mlsanity.com/paper/2211.12075/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 25 references that are in the map.
- First posted on arXiv 22 Nov 2022.

## Builds on (most cited first, 18 of 18)

- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [Prioritized Experience Replay](https://mlsanity.com/paper/1511.05952/) (2015)
- [Counterfactual Multi-Agent Policy Gradients](https://mlsanity.com/paper/1705.08926/) (2017)
- [QMIX: Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1803.11485/) (2018)
- [The StarCraft Multi-Agent Challenge](https://mlsanity.com/paper/1902.04043/) (2019)
- [Learning to Communicate with Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1605.06676/) (2016)
- [Value-Decomposition Networks For Cooperative Multi-Agent Learning](https://mlsanity.com/paper/1706.05296/) (2017)
- [QTRAN: Learning to Factorize with Transformation for Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1905.05408/) (2019)
- [QPLEX: Duplex Dueling Multi-Agent Q-Learning](https://mlsanity.com/paper/2008.01062/) (2020)
- [Weighted QMIX: Expanding Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2006.10800/) (2020)
- [MAVEN: Multi-Agent Variational Exploration](https://mlsanity.com/paper/1910.07483/) (2019)
- [A Deeper Look at Experience Replay](https://mlsanity.com/paper/1712.01275/) (2017)
- [Deep Coordination Graphs](https://mlsanity.com/paper/1910.00091/) (2019)
- [Qatten: A General Framework for Cooperative Multiagent Reinforcement Learning](https://mlsanity.com/paper/2002.03939/) (2020)
- [UneVEn: Universal Value Exploration for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2010.02974/) (2020)
- [Multiagent Soft Q-Learning](https://mlsanity.com/paper/1804.09817/) (2018)
- [Q-value Path Decomposition for Deep Multiagent Reinforcement Learning](https://mlsanity.com/paper/2002.03950/) (2020)
- [SMIX(λ): Enhancing Centralized Value Functions for Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1911.04094/) (2019)

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

- [Counterfactual Conservative Q Learning for Offline Multi-agent Reinforcement Learning](https://mlsanity.com/paper/2309.12696/) (2023)
- [Retaining Suboptimal Actions to Follow Shifting Optima in Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2602.17062/) (2026)
- [Adaptive Value Decomposition with Greedy Marginal Contribution Computation for Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2302.06872/) (2023)
- [Breakthrough the Suboptimal Stable Point in Value-Factorization-Based Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2604.05297/) (2026)

## Abstract (arXiv)

Due to the representation limitation of the joint Q value function, multi-agent reinforcement learning methods with linear value decomposition (LVD) or monotonic value decomposition (MVD) suffer from relative overgeneralization. As a result, they can not ensure optimal consistency (i.e., the correspondence between individual greedy actions and the maximal true Q value). In this paper, we derive the expression of the joint Q value function of LVD and MVD. According to the expression, we draw a transition diagram, where each self-transition node (STN) is a possible convergence. To ensure optimal consistency, the optimal node is required to be the unique STN. Therefore, we propose the greedy-based value representation (GVR), which turns the optimal node into an STN via inferior target shaping and further eliminates the non-optimal STNs via superior experience replay. In addition, GVR achieves an adaptive trade-off between optimality and stability. Our method outperforms state-of-the-art baselines in experiments on various benchmarks. Theoretical proofs and empirical results on matrix games demonstrate that GVR ensures optimal consistency under sufficient exploration.