# Best Possible Q-Learning

arXiv: https://arxiv.org/abs/2302.01188 · HTML: https://mlsanity.com/paper/2302.01188/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 36 references that are in the map.
- First posted on arXiv 2 Feb 2023.

## Builds on (most cited first, 23 of 23)

- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [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)
- [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)
- [Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithms](https://mlsanity.com/paper/1911.10635/) (2019)
- [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)
- [Is Independent Learning All You Need in the StarCraft Multi-Agent Challenge?](https://mlsanity.com/paper/2011.09533/) (2020)
- [QPLEX: Duplex Dueling Multi-Agent Q-Learning](https://mlsanity.com/paper/2008.01062/) (2020)
- [Actor-Attention-Critic for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1810.02912/) (2018)
- [Google Research Football: A Novel Reinforcement Learning Environment](https://mlsanity.com/paper/1907.11180/) (2019)
- [Weighted QMIX: Expanding Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2006.10800/) (2020)
- [Fully Decentralized Multi-Agent Reinforcement Learning with Networked Agents](https://mlsanity.com/paper/1802.08757/) (2018)
- [FACMAC: Factored Multi-Agent Centralised Policy Gradients](https://mlsanity.com/paper/2003.06709/) (2020)
- [Off-Policy Multi-Agent Decomposed Policy Gradients](https://mlsanity.com/paper/2007.12322/) (2020)
- [Rethinking the Implementation Tricks and Monotonicity Constraint in Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2102.03479/) (2021)
- [Multi-Agent Reinforcement Learning for Active Voltage Control on Power Distribution Networks](https://mlsanity.com/paper/2110.14300/) (2021)
- [A Cooperative Multi-Agent Reinforcement Learning Framework for Resource Balancing in Complex Logistics Network](https://mlsanity.com/paper/1903.00714/) (2019)
- [Multi-Agent Trust Region Policy Optimization](https://mlsanity.com/paper/2010.07916/) (2020)
- [Divergence-Regularized Multi-Agent Actor-Critic](https://mlsanity.com/paper/2110.00304/) (2021)
- [Iterated Reasoning with Mutual Information in Cooperative and Byzantine Decentralized Teaming](https://mlsanity.com/paper/2201.08484/) (2022)
- [MA2QL: A Minimalist Approach to Fully Decentralized Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2209.08244/) (2022)

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

- [An Introduction to Centralized Training for Decentralized Execution in Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2409.03052/) (2024)
- [Fully Decentralized Cooperative Multi-Agent Reinforcement Learning: A Survey](https://mlsanity.com/paper/2401.04934/) (2024)
- [Belief States for Cooperative Multi-Agent Reinforcement Learning under Partial Observability](https://mlsanity.com/paper/2504.08417/) (2025)
- [Local Reinforcement Learning with Action-Conditioned Root Mean Squared Q-Functions](https://mlsanity.com/paper/2510.06649/) (2025)

## Abstract (arXiv)

Fully decentralized learning, where the global information, i.e., the actions of other agents, is inaccessible, is a fundamental challenge in cooperative multi-agent reinforcement learning. However, the convergence and optimality of most decentralized algorithms are not theoretically guaranteed, since the transition probabilities are non-stationary as all agents are updating policies simultaneously. To tackle this challenge, we propose best possible operator, a novel decentralized operator, and prove that the policies of agents will converge to the optimal joint policy if each agent independently updates its individual state-action value by the operator. Further, to make the update more efficient and practical, we simplify the operator and prove that the convergence and optimality still hold with the simplified one. By instantiating the simplified operator, the derived fully decentralized algorithm, best possible Q-learning (BQL), does not suffer from non-stationarity. Empirically, we show that BQL achieves remarkable improvement over baselines in a variety of cooperative multi-agent tasks.