Learning Multi-Agent Coordination via Sheaf-ADMM

2026-05-29

AI Summary

This work addresses the challenge of effective multi-agent coordination under partial observability and incomplete information. The authors propose a differentiable cooperative framework grounded in cellular sheaf theory, wherein inputs are decomposed into overlapping local views. Each agent parameterizes a convex subproblem via a neural encoder, and coordination is achieved through a differentiable ADMM algorithm augmented with heterogeneous consensus constraints. The entire system is trained end-to-end by unrolling the optimization process, offering both interpretability and intervenability. Empirical results demonstrate significant performance gains over baseline methods on maze navigation, MNIST classification, and Sudoku solving tasks. Notably, the approach exhibits superior robustness under distributional shift and substantially outperforms MPNN models on Sudoku with comparable parameter counts.

Abstract

We present a differentiable optimization framework for multi-agent coordination. An input is decomposed into overlapping local views, each processed by an agent that solves a convex subproblem parameterized by a neural encoder. Agents coordinate through the Alternating Direction Method of Multipliers (ADMM) with inter-agent constraints specified by a cellular sheaf. The sheaf specifies which aspects of neighboring solutions must agree, allowing for heterogeneous notions of global consensus. Backpropagating through the unrolled optimization jointly trains all components of the multi-agent system. We evaluate on maze pathfinding, image classification, and Sudoku, where agents with individually insufficient local views learn to coordinate to produce correct global outputs. On MNIST, the local-view decomposition yields improved robustness to distribution shifts relative to a standard CNN. On Sudoku, the optimization-derived structure yields markedly higher solve rates than parameter-matched MPNN baselines. Finally, the ADMM structure exposes distinct primal, consensus, and dual state variables, opening the coordination dynamics to direct analysis and intervention -- a property unavailable in standard message-passing architectures.

Problem

• multi-agent coordination
• local views
• global consensus
• heterogeneous agents
• distributed optimization

Innovation

• Sheaf-ADMM
• differentiable optimization
• multi-agent coordination
• heterogeneous consensus
• unrolled optimization