# Mixed Q-Functionals: Advancing Value-Based Methods in Cooperative MARL with Continuous Action Domains

arXiv: https://arxiv.org/abs/2402.07752 · HTML: https://mlsanity.com/paper/2402.07752/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 30 references that are in the map.
- First posted on arXiv 12 Feb 2024.

## Builds on (most cited first, 13 of 13)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [The Surprising Effectiveness of PPO in Cooperative, Multi-Agent Games](https://mlsanity.com/paper/2103.01955/) (2021)
- [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)
- [Emergence of Grounded Compositional Language in Multi-Agent Populations](https://mlsanity.com/paper/1703.04908/) (2017)
- [PettingZoo: Gym for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2009.14471/) (2020)
- [Benchmarking Multi-Agent Deep Reinforcement Learning Algorithms in Cooperative Tasks](https://mlsanity.com/paper/2006.07869/) (2020)
- [Weighted QMIX: Expanding Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2006.10800/) (2020)
- [FACMAC: Factored Multi-Agent Centralised Policy Gradients](https://mlsanity.com/paper/2003.06709/) (2020)
- [Impact of Relational Networks in Multi-Agent Learning: A Value-Based Factorization View](https://mlsanity.com/paper/2310.12912/) (2023)

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

- [Investigating Adaptive Tuning of Assistive Exoskeletons Using Offline Reinforcement Learning: Challenges and Insights](https://mlsanity.com/paper/2505.00201/) (2025)

## Abstract (arXiv)

Tackling multi-agent learning problems efficiently is a challenging task in continuous action domains. While value-based algorithms excel in sample efficiency when applied to discrete action domains, they are usually inefficient when dealing with continuous actions. Policy-based algorithms, on the other hand, attempt to address this challenge by leveraging critic networks for guiding the learning process and stabilizing the gradient estimation. The limitations in the estimation of true return and falling into local optima in these methods result in inefficient and often sub-optimal policies. In this paper, we diverge from the trend of further enhancing critic networks, and focus on improving the effectiveness of value-based methods in multi-agent continuous domains by concurrently evaluating numerous actions. We propose a novel multi-agent value-based algorithm, Mixed Q-Functionals (MQF), inspired from the idea of Q-Functionals, that enables agents to transform their states into basis functions. Our algorithm fosters collaboration among agents by mixing their action-values. We evaluate the efficacy of our algorithm in six cooperative multi-agent scenarios. Our empirical findings reveal that MQF outperforms four variants of Deep Deterministic Policy Gradient through rapid action evaluation and increased sample efficiency.