PEnGUiN: Partially Equivariant Graph NeUral Networks for Sample Efficient MARL

2025-03-19

AI Summary

In real-world multi-agent reinforcement learning (MARL), environmental asymmetries—arising from external forces, measurement errors, and systemic biases—severely degrade the sample efficiency and generalization of equivariant graph neural networks (EGNNs). To address this, we propose Partially Equivariant Graph Neural Networks (PEGNNs), the first framework to formally characterize partial equivariance across four dimensions: subgroups, features, spatial regions, and approximations—establishing a continuous spectrum from full equivariance to complete non-equivariance. PEGNNs unify EGNNs and standard GNNs within a single architecture via group-representation-driven differentiable subgroup masking, hierarchical feature disentanglement, and hybrid equivariant message passing. Evaluated on multiple MARL benchmarks exhibiting realistic asymmetries, PEGNNs achieve up to 42% higher sample efficiency than EGNNs and up to 67% higher than standard GNNs, while significantly improving generalization and robustness.

Technology Category

Multiagent Systems: Adversarial AgentsMachine Learning: Graph-based Machine LearningGame Theory and Economic Paradigms: Adversarial Learning

Application Category

Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphsSemantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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 extit{Partially 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.

Problem

• Addresses asymmetries in real-world MARL environments
• Introduces PEnGUiN for partial equivariance in graph neural networks
• Improves robustness and sample efficiency in asymmetric MARL scenarios

Innovation

• Introduces Partially Equivariant Graph Neural Networks (PEnGUiN)
• Addresses real-world asymmetries in MARL environments
• Unifies EGNN and GNN representations in one framework