Pairwise is Not Enough: Hypergraph Neural Networks for Multi-Agent Pathfinding

TL;DR

This work tackles multi-agent pathfinding (MAPF) by moving beyond pairwise interactions to explicit higher-order group dynamics through directed hypergraphs. The HMAGAT architecture replaces GNN-based policies with Hypergraph Attention Networks (HGNNs) and introduces multiple hypergraph-generation strategies to capture group interactions efficiently, mitigating attention dilution in dense environments. Through imitation-learning training, online data aggregation, post-training refinement, and a temperature-sampling module, HMAGAT achieves state-of-the-art results with far fewer parameters and data than prior learning-based solvers. The empirical analysis demonstrates that hypergraph biases enable superior coordination, especially in dense maps, and that higher-order representations can significantly reduce sample complexity while improving solution quality. Overall, the results advocate hypergraph-based interaction modeling as a powerful, scalable approach for highly coupled multi-agent problems.

Abstract

Multi-Agent Path Finding (MAPF) is a representative multi-agent coordination problem, where multiple agents are required to navigate to their respective goals without collisions. Solving MAPF optimally is known to be NP-hard, leading to the adoption of learning-based approaches to alleviate the online computational burden. Prevailing approaches, such as Graph Neural Networks (GNNs), are typically constrained to pairwise message passing between agents. However, this limitation leads to suboptimal behaviours and critical issues, such as attention dilution, particularly in dense environments where group (i.e. beyond just two agents) coordination is most critical. Despite the importance of such higher-order interactions, existing approaches have not been able to fully explore them. To address this representational bottleneck, we introduce HMAGAT (Hypergraph Multi-Agent Attention Network), a novel architecture that leverages attentional mechanisms over directed hypergraphs to explicitly capture group dynamics. Empirically, HMAGAT establishes a new state-of-the-art among learning-based MAPF solvers: e.g., despite having just 1M parameters and being trained on 100$\times$ less data, it outperforms the current SoTA 85M parameter model. Through detailed analysis of HMAGAT's attention values, we demonstrate how hypergraph representations mitigate the attention dilution inherent in GNNs and capture complex interactions where pairwise methods fail. Our results illustrate that appropriate inductive biases are often more critical than the training data size or sheer parameter count for multi-agent problems.

Figures (11)

• Figure 1: (a) MAPF requires group interactions. (i) The SoC-optimal (sum-of-costs) group interaction-based solution. (iii-v) Pairwise interactions with agent A, showing the optimal paths when agent pairs are isolated. (ii) Combination of the pairwise solutions. This solution is sub-optimal compared to the group interaction-based solution. (b) Group interaction modelling has been previously unexplored. Positioning of MAPF solvers with respect to their interaction modelling. (c) HMAGAT achieves state-of-the-art performance. Radar plot comparing learnt MAPF solvers, showing average solution quality and scalability (both the higher, the better) across different small mapsand agent densities, and a focused view on the highest agent density (High AD) scenarios. Details of the metrics are in \ref{['sec:appendix-radar-plot']}.
• Figure 2: Overview of HMAGAT. (a) We collect demonstrations using an expert solver over 21K instances. (b) For each timestep, we extract a directed hypergraph representation (head agent shown with bold outline here). (c) These are used to train our HGNN-based model. (d) Post-training, we train the model using expert trajectories over intermediate instances, to improve solution quality. A temperature sampler is also trained to make the model more confident.
• Figure 3: Going from (a) strict partitioning to (b) overlapping groups.
• Figure 4: Evaluation of the learning-based MAPF policies, averaged over $128$ instances. Transparent regions represent $95\%$ confidence intervals. SoC is reported relative to lacam3 (w/ 30s time limit).
• Figure 5: Ablation study. We start from MAGAT and incrementally add components to reach HMAGAT. We plot the failure rate and Rel. SoC (both the lower the better), over the highest agent density scenarios of the small maps.