# Effects of Spectral Normalization in Multi-agent Reinforcement Learning

arXiv: https://arxiv.org/abs/2212.05331 · HTML: https://mlsanity.com/paper/2212.05331/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 38 references that are in the map.
- First posted on arXiv 10 Dec 2022.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [Hindsight Experience Replay](https://mlsanity.com/paper/1707.01495/) (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)
- [MOPO: Model-based Offline Policy Optimization](https://mlsanity.com/paper/2005.13239/) (2020)
- [The StarCraft Multi-Agent Challenge](https://mlsanity.com/paper/1902.04043/) (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)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [QTRAN: Learning to Factorize with Transformation for Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1905.05408/) (2019)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Benchmarking Multi-Agent Deep Reinforcement Learning Algorithms in Cooperative Tasks](https://mlsanity.com/paper/2006.07869/) (2020)
- [MAVEN: Multi-Agent Variational Exploration](https://mlsanity.com/paper/1910.07483/) (2019)
- [RODE: Learning Roles to Decompose Multi-Agent Tasks](https://mlsanity.com/paper/2010.01523/) (2020)
- [Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1512.07666/) (2015)
- [The Numerics of GANs](https://mlsanity.com/paper/1705.10461/) (2017)
- [Spectral Normalisation for Deep Reinforcement Learning: an Optimisation Perspective](https://mlsanity.com/paper/2105.05246/) (2021)
- [UneVEn: Universal Value Exploration for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2010.02974/) (2020)
- [Competitive Gradient Descent](https://mlsanity.com/paper/1905.12103/) (2019)
- [Tesseract: Tensorised Actors for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2106.00136/) (2021)
- [Generalization in Cooperative Multi-Agent Systems](https://mlsanity.com/paper/2202.00104/) (2022)
- [Symmetry Learning for Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1706.02999/) (2017)

## Built on by (most cited first, 6 of 6)

- [Normalization Enhances Generalization in Visual Reinforcement Learning](https://mlsanity.com/paper/2306.00656/) (2023)
- [Alpha Elimination: Using Deep Reinforcement Learning to Reduce Fill-In during Sparse Matrix Decomposition](https://mlsanity.com/paper/2310.09852/) (2023)
- [Angle based dynamic learning rate for gradient descent](https://mlsanity.com/paper/2304.10457/) (2023)
- [Unifying Agent Interaction and World Information for Multi-agent Coordination](https://mlsanity.com/paper/2509.25550/) (2025)
- [SignMuon: Communication-Efficient Distributed Muon Optimization](https://mlsanity.com/paper/2605.16311/) (2026)
- [Nonnegative Low-Rank Tensor Completion via Dual Formulation with Applications to Image and Video Completion](https://mlsanity.com/paper/2305.07976/) (2023)

## Abstract (arXiv)

A reliable critic is central to on-policy actor-critic learning. But it becomes challenging to learn a reliable critic in a multi-agent sparse reward scenario due to two factors: 1) The joint action space grows exponentially with the number of agents 2) This, combined with the reward sparseness and environment noise, leads to large sample requirements for accurate learning. We show that regularising the critic with spectral normalization (SN) enables it to learn more robustly, even in multi-agent on-policy sparse reward scenarios. Our experiments show that the regularised critic is quickly able to learn from the sparse rewarding experience in the complex SMAC and RWARE domains. These findings highlight the importance of regularisation in the critic for stable learning.