# Fixing Incomplete Value Function Decomposition for Multi-Agent Reinforcement Learning

arXiv: https://arxiv.org/abs/2505.10484 · HTML: https://mlsanity.com/paper/2505.10484/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 24 references that are in the map.
- First posted on arXiv 15 May 2025.

## Builds on (most cited first, 14 of 14)

- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [Deep Reinforcement Learning at the Edge of the Statistical Precipice](https://mlsanity.com/paper/2108.13264/) (2021)
- [Dueling Network Architectures for Deep Reinforcement Learning](https://mlsanity.com/paper/1511.06581/) (2015)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [Value-Decomposition Networks For Cooperative Multi-Agent Learning](https://mlsanity.com/paper/1706.05296/) (2017)
- [Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2003.08839/) (2020)
- [QTRAN: Learning to Factorize with Transformation for Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1905.05408/) (2019)
- [On the Utility of Learning about Humans for Human-AI Coordination](https://mlsanity.com/paper/1910.05789/) (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)
- [SMACv2: An Improved Benchmark for Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2212.07489/) (2022)
- [JaxMARL: Multi-Agent RL Environments and Algorithms in JAX](https://mlsanity.com/paper/2311.10090/) (2023)
- [Towards Understanding Cooperative Multi-Agent Q-Learning with Value Factorization](https://mlsanity.com/paper/2006.00587/) (2020)
- [On Stateful Value Factorization in Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2408.15381/) (2024)

## Built on by (most cited first, 1 of 1)

- [Learning Decentralized LLM Collaboration with Multi-Agent Actor Critic](https://mlsanity.com/paper/2601.21972/) (2026)

## Abstract (arXiv)

Value function decomposition methods for cooperative multi-agent reinforcement learning compose joint values from individual per-agent utilities, and train them using a joint objective. To ensure that the action selection process between individual utilities and joint values remains consistent, it is imperative for the composition to satisfy the individual-global max (IGM) property. Although satisfying IGM itself is straightforward, most existing methods (e.g., VDN, QMIX) have limited representation capabilities and are unable to represent the full class of IGM values, and the one exception that has no such limitation (QPLEX) is unnecessarily complex. In this work, we present a simple formulation of the full class of IGM values that naturally leads to the derivation of QFIX, a novel family of value function decomposition models that expand the representation capabilities of prior models by means of a thin "fixing" layer. We derive multiple variants of QFIX, and implement three variants in two well-known multi-agent frameworks. We perform an empirical evaluation on multiple SMACv2 and Overcooked environments, which confirms that QFIX (i) succeeds in enhancing the performance of prior methods, (ii) learns more stably and performs better than its main competitor QPLEX, and (iii) achieves this while employing the simplest and smallest mixing models.