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Reliable and Efficient Multi-Agent Coordination via Graph Neural Network Variational Autoencoders

Yue Meng, Nathalie Majcherczyk, Wenliang Liu, Scott Kiesel, Chuchu Fan, Federico Pecora

TL;DR

The paper addresses scalable multi-agent coordination by formulating the problem on a coordination graph and learning a distribution over feasible, constraint-satisfying assignments with a Graph Neural Network Variational Autoencoder (GNN-VAE). Ground-truth solutions are generated via MILP, and the GNN-VAE encodes these into a latent space from which diverse, feasible assignments are decoded; a two-branch design guarantees acyclic and density constraints. Empirically, the approach delivers near-oracle quality on problems with up to 250 robots while achieving 10–20× faster inference than strong baselines, and demonstrates strong generalization to larger scales and unseen obstacle configurations. The work advances practical, reliable, and scalable explicit coordination for dense multi-robot systems, with potential impact on automated warehouses and other high-traffic environments.

Abstract

Multi-agent coordination is crucial for reliable multi-robot navigation in shared spaces such as automated warehouses. In regions of dense robot traffic, local coordination methods may fail to find a deadlock-free solution. In these scenarios, it is appropriate to let a central unit generate a global schedule that decides the passing order of robots. However, the runtime of such centralized coordination methods increases significantly with the problem scale. In this paper, we propose to leverage Graph Neural Network Variational Autoencoders (GNN-VAE) to solve the multi-agent coordination problem at scale faster than through centralized optimization. We formulate the coordination problem as a graph problem and collect ground truth data using a Mixed-Integer Linear Program (MILP) solver. During training, our learning framework encodes good quality solutions of the graph problem into a latent space. At inference time, solution samples are decoded from the sampled latent variables, and the lowest-cost sample is selected for coordination. Finally, the feasible proposal with the highest performance index is selected for the deployment. By construction, our GNN-VAE framework returns solutions that always respect the constraints of the considered coordination problem. Numerical results show that our approach trained on small-scale problems can achieve high-quality solutions even for large-scale problems with 250 robots, being much faster than other baselines. Project page: https://mengyuest.github.io/gnn-vae-coord

Reliable and Efficient Multi-Agent Coordination via Graph Neural Network Variational Autoencoders

TL;DR

The paper addresses scalable multi-agent coordination by formulating the problem on a coordination graph and learning a distribution over feasible, constraint-satisfying assignments with a Graph Neural Network Variational Autoencoder (GNN-VAE). Ground-truth solutions are generated via MILP, and the GNN-VAE encodes these into a latent space from which diverse, feasible assignments are decoded; a two-branch design guarantees acyclic and density constraints. Empirically, the approach delivers near-oracle quality on problems with up to 250 robots while achieving 10–20× faster inference than strong baselines, and demonstrates strong generalization to larger scales and unseen obstacle configurations. The work advances practical, reliable, and scalable explicit coordination for dense multi-robot systems, with potential impact on automated warehouses and other high-traffic environments.

Abstract

Multi-agent coordination is crucial for reliable multi-robot navigation in shared spaces such as automated warehouses. In regions of dense robot traffic, local coordination methods may fail to find a deadlock-free solution. In these scenarios, it is appropriate to let a central unit generate a global schedule that decides the passing order of robots. However, the runtime of such centralized coordination methods increases significantly with the problem scale. In this paper, we propose to leverage Graph Neural Network Variational Autoencoders (GNN-VAE) to solve the multi-agent coordination problem at scale faster than through centralized optimization. We formulate the coordination problem as a graph problem and collect ground truth data using a Mixed-Integer Linear Program (MILP) solver. During training, our learning framework encodes good quality solutions of the graph problem into a latent space. At inference time, solution samples are decoded from the sampled latent variables, and the lowest-cost sample is selected for coordination. Finally, the feasible proposal with the highest performance index is selected for the deployment. By construction, our GNN-VAE framework returns solutions that always respect the constraints of the considered coordination problem. Numerical results show that our approach trained on small-scale problems can achieve high-quality solutions even for large-scale problems with 250 robots, being much faster than other baselines. Project page: https://mengyuest.github.io/gnn-vae-coord

Paper Structure

This paper contains 13 sections, 1 theorem, 10 equations, 7 figures.

Table of Contents

  1. INTRODUCTION
  2. RELATED WORK
  3. PRELIMINARIES
  4. Problem Formulation
  5. TECHNICAL APPROACH
  6. MILP formulation for assignment optimization
  7. Assignment prediction using GNN-VAE
  8. EXPERIMENTS
  9. Main results on small-scale problems
  10. Generalizability and scalability to large-scale problems
  11. Test on out-of-distribution data in simulation
  12. Ablation studies
  13. CONCLUSIONS

Key Result

Proposition 1

Given a mixed graph $G=(V,E,S)\in\mathcal{G}$ with disjointed directed edges $E$ and undirected edges $S$ and $G'=(V,E)\in\mathcal{G}_d$ a directed acyclic graph (DAG), denote the transformation from the mixed graph and node bids to a new directed graph as $\mathcal{T}:\mathcal{G}\times\mathcal{B}_V

Figures (7)

  • Figure 1: Illustration for the coordination graph.
  • Figure 2: Learning framework: The GNN-VAE first encodes the assignment via graph convolution and graph max pooling to a latent embedding. The sampled latent code is sent to the decoder and the two-branch MLP to get the predicted assignment.
  • Figure 3: Main comparisons for solution quality and computation runtime under different cost functions.
  • Figure 4: Performance over larger graphs.
  • Figure 5: Runtime breakdown for GNN-VAE at inference stage.
  • ...and 2 more figures

Theorems & Definitions (2)

  • Proposition 1
  • proof