Fixing Incomplete Value Function Decomposition for Multi-Agent Reinforcement Learning (2505.10484v1)

Abstract: 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.

Fixing Incomplete Value Function Decomposition for Multi-Agent Reinforcement Learning

The paper "Fixing Incomplete Value Function Decomposition for Multi-Agent Reinforcement Learning" introduces a novel approach to enhance the representation capabilities of existing value function decomposition methods used in cooperative multi-agent reinforcement learning (MARL). The authors propose a model called QFIX, which addresses the limitations of existing methods like VDN, QMIX, and QPLEX in terms of their ability to fully satisfy the Individual-Global Max (IGM) property necessary for effective decentralized action selection.

Overview

Value function decomposition methods in MARL aim to construct joint values from individual per-agent utilities, ensuring that decision processes remain consistent and satisfying the IGM property. IGM ensures that the decision-making process ties the decentralized agent utilities to the centralized joint values properly. However, existing methods such as VDN and QMIX lack the expressiveness to represent the full class of IGM-complete values due to their restricted function classes, while QPLEX, despite its IGM-completeness, is unnecessarily complex.

The authors present a simple formulation of IGM-complete value functions that leads to the development of QFIX—a family of models that improve prior methods' capabilities by introducing a "fixing" layer. QFIX variants such as QFIX-sum and QFIX-mono are derived by expanding the representation capabilities of VDN and QMIX, respectively. Additionally, a variant called QFIX-lin is introduced, which blends QFIX-sum with elements from QPLEX.

Numerical Results

The empirical evaluation conducted on SMACv2 and Overcooked environments demonstrates strong performance results for QFIX models:

1. QFIX significantly enhances the performance of VDN and QMIX in terms of stability and convergence.
2. The models achieve competitive or superior performance to QPLEX while employing simpler and smaller mixing architectures.
3. Ablation studies confirm that the superior performance of QFIX models stems from intrinsic mixing strategies rather than merely expanding baseline parameters.

These results underline QFIX's efficiency in learning stable decentralized policies while maintaining strong numerical performance.

Implications and Future Directions

QFIX introduces a new avenue for exploring decomposed value functions in MARL. Its simplicity and effectiveness suggest possible expansions to other domains of reinforcement learning where decentralized execution is critical. Such applications might include complex coordination tasks in dynamic environments like robotic swarms or decentralized network control systems.

The theoretical implications pertain to the simplification of IGM-complete models, suggesting that future work might focus on minimalistic yet powerful architectures that further improve computational efficiency without sacrificing decision-making integrity. Additionally, exploring variants of QFIX in larger, distributed multi-agent settings could yield insights into scaling and adapting MARL methodologies.

By addressing the limitations of existing approaches, this paper provides an important stepping stone towards more efficient and effective MARL frameworks, showcasing the ability to bridge gaps between centralized training and decentralized execution. Future research may explore the generalized applicability of the QFIX formulation across varied MARL settings, potentially leading to new developments in reinforcement learning theory and practice.