# PEnGUiN: Partially Equivariant Graph NeUral Networks for Sample Efficient MARL

arXiv: https://arxiv.org/abs/2503.15615 · HTML: https://mlsanity.com/paper/2503.15615/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 26 references that are in the map.
- First posted on arXiv 19 Mar 2025.

## Builds on (most cited first, 22 of 22)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups](https://mlsanity.com/paper/2104.09459/) (2021)
- [MDP Homomorphic Networks: Group Symmetries in Reinforcement Learning](https://mlsanity.com/paper/2006.16908/) (2020)
- [Approximately Equivariant Networks for Imperfectly Symmetric Dynamics](https://mlsanity.com/paper/2201.11969/) (2022)
- [Residual Pathway Priors for Soft Equivariance Constraints](https://mlsanity.com/paper/2112.01388/) (2021)
- [Approximation-Generalization Trade-offs under (Approximate) Group Equivariance](https://mlsanity.com/paper/2305.17592/) (2023)
- [Relaxing Equivariance Constraints with Non-stationary Continuous Filters](https://mlsanity.com/paper/2204.07178/) (2022)
- [The Surprising Effectiveness of Equivariant Models in Domains with Latent Symmetry](https://mlsanity.com/paper/2211.09231/) (2022)
- [Multi-Agent MDP Homomorphic Networks](https://mlsanity.com/paper/2110.04495/) (2021)
- [Discovering Symmetry Breaking in Physical Systems with Relaxed Group Convolution](https://mlsanity.com/paper/2310.02299/) (2023)
- [A General Theory of Correct, Incorrect, and Extrinsic Equivariance](https://mlsanity.com/paper/2303.04745/) (2023)
- [Approximately Equivariant Graph Networks](https://mlsanity.com/paper/2308.10436/) (2023)
- [Subequivariant Graph Reinforcement Learning in 3D Environments](https://mlsanity.com/paper/2305.18951/) (2023)
- [Leveraging Partial Symmetry for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2401.00167/) (2023)
- [Almost Equivariance via Lie Algebra Convolutions](https://mlsanity.com/paper/2310.13164/) (2023)
- [Boosting Sample Efficiency and Generalization in Multi-agent Reinforcement Learning via Equivariance](https://mlsanity.com/paper/2410.02581/) (2024)
- [Approximate Equivariance in Reinforcement Learning](https://mlsanity.com/paper/2411.04225/) (2024)
- [Relaxed Equivariant Graph Neural Networks](https://mlsanity.com/paper/2407.20471/) (2024)
- [Symmetry-Based Structured Matrices for Efficient Approximately Equivariant Networks](https://mlsanity.com/paper/2409.11772/) (2024)

## Built on by (most cited first, 2 of 2)

- [cMALC-D: Contextual Multi-Agent LLM-Guided Curriculum Learning with Diversity-Based Context Blending](https://mlsanity.com/paper/2508.20818/) (2025)
- [Local-Canonicalization Equivariant Graph Neural Networks for Sample-Efficient and Generalizable Swarm Robot Control](https://mlsanity.com/paper/2509.14431/) (2025)

## Abstract (arXiv)

Equivariant Graph Neural Networks (EGNNs) have emerged as a promising approach in Multi-Agent Reinforcement Learning (MARL), leveraging symmetry guarantees to greatly improve sample efficiency and generalization. However, real-world environments often exhibit inherent asymmetries arising from factors such as external forces, measurement inaccuracies, or intrinsic system biases. This paper introduces textitPartially Equivariant Graph NeUral Networks (PEnGUiN), a novel architecture specifically designed to address these challenges. We formally identify and categorize various types of partial equivariance relevant to MARL, including subgroup equivariance, feature-wise equivariance, regional equivariance, and approximate equivariance. We theoretically demonstrate that PEnGUiN is capable of learning both fully equivariant (EGNN) and non-equivariant (GNN) representations within a unified framework. Through extensive experiments on a range of MARL problems incorporating various asymmetries, we empirically validate the efficacy of PEnGUiN. Our results consistently demonstrate that PEnGUiN outperforms both EGNNs and standard GNNs in asymmetric environments, highlighting their potential to improve the robustness and applicability of graph-based MARL algorithms in real-world scenarios.