Learning Multi-Agent Coordination via Sheaf-ADMM
This work provides a novel differentiable optimization framework for multi-agent coordination, offering a structured approach to global consensus for researchers and practitioners working on distributed AI systems.
This paper introduces a differentiable optimization framework, Sheaf-ADMM, for multi-agent coordination where agents with overlapping local views solve convex subproblems and coordinate via ADMM with sheaf-specified inter-agent constraints. The framework enables agents to learn to coordinate for correct global outputs, demonstrating improved robustness to distribution shifts on MNIST and markedly higher Sudoku solve rates compared to parameter-matched MPNN baselines.
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.