# Taming Multi-Agent Reinforcement Learning with Estimator Variance Reduction

arXiv: https://arxiv.org/abs/2209.01054 · HTML: https://mlsanity.com/paper/2209.01054/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 29 references that are in the map.
- First posted on arXiv 2 Sep 2022.

## Builds on (most cited first, 21 of 21)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [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)
- [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)
- [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)
- [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)
- [SMARTS: Scalable Multi-Agent Reinforcement Learning Training School for Autonomous Driving](https://mlsanity.com/paper/2010.09776/) (2020)
- [Shared Experience Actor-Critic for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2006.07169/) (2020)
- [Multiagent Bidirectionally-Coordinated Nets: Emergence of Human-level Coordination in Learning to Play StarCraft Combat Games](https://mlsanity.com/paper/1703.10069/) (2017)
- [Q-Prop: Sample-Efficient Policy Gradient with An Off-Policy Critic](https://mlsanity.com/paper/1611.02247/) (2016)
- [Settling the Variance of Multi-Agent Policy Gradients](https://mlsanity.com/paper/2108.08612/) (2021)
- [Multi-Agent Determinantal Q-Learning](https://mlsanity.com/paper/2006.01482/) (2020)
- [Revisiting Some Common Practices in Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2206.07505/) (2022)
- [Learning in Nonzero-Sum Stochastic Games with Potentials](https://mlsanity.com/paper/2103.09284/) (2021)
- [Decentralised Learning in Systems with Many, Many Strategic Agents](https://mlsanity.com/paper/1803.05028/) (2018)
- [LIGS: Learnable Intrinsic-Reward Generation Selection for Multi-Agent Learning](https://mlsanity.com/paper/2112.02618/) (2021)

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

- [From Grunts to Lexicons: Emergent Language from Cooperative Foraging](https://mlsanity.com/paper/2505.12872/) (2025)

## Abstract (arXiv)

Centralised training with decentralised execution (CT-DE) serves as the foundation of many leading multi-agent reinforcement learning (MARL) algorithms. Despite its popularity, it suffers from a critical drawback due to its reliance on learning from a single sample of the joint-action at a given state. As agents explore and update their policies during training, these single samples may poorly represent the actual joint-policy of the system of agents leading to high variance gradient estimates that hinder learning. To address this problem, we propose an enhancement tool that accommodates any actor-critic MARL method. Our framework, Performance Enhancing Reinforcement Learning Apparatus (PERLA), introduces a sampling technique of the agents' joint-policy into the critics while the agents train. This leads to TD updates that closely approximate the true expected value under the current joint-policy rather than estimates from a single sample of the joint-action at a given state. This produces low variance and precise estimates of expected returns, minimising the variance in the critic estimators which typically hinders learning. Moreover, as we demonstrate, by eliminating much of the critic variance from the single sampling of the joint policy, PERLA enables CT-DE methods to scale more efficiently with the number of agents. Theoretically, we prove that PERLA reduces variance in value estimates similar to that of decentralised training while maintaining the benefits of centralised training. Empirically, we demonstrate PERLA's superior performance and ability to reduce estimator variance in a range of benchmarks including Multi-agent Mujoco, and StarCraft II Multi-agent Challenge.