Asynchronous Nonlinear Sheaf Diffusion for Multi-Agent Coordination
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912620596953088 |
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| author | Zhao, Yichen Hanks, Tyler Riess, Hans Cohen, Samuel Hale, Matthew Fairbanks, James |
| author_facet | Zhao, Yichen Hanks, Tyler Riess, Hans Cohen, Samuel Hale, Matthew Fairbanks, James |
| contents | Cellular sheaves and sheaf Laplacians provide a far-reaching generalization of graphs and graph Laplacians, resulting in a wide array of applications ranging from machine learning to multi-agent control. In the context of multi-agent systems, so called coordination sheaves provide a unifying formalism that models heterogeneous agents and coordination goals over undirected communication topologies, and applying sheaf diffusion drives agents to achieve their coordination goals. Existing literature on sheaf diffusion assumes that agents can communicate and compute updates synchronously, which is an unrealistic assumption in many scenarios where communication delays or heterogeneous agents with different compute capabilities cause disagreement among agents. To address these challenges, we introduce asynchronous nonlinear sheaf diffusion. Specifically, we show that under mild assumptions on the coordination sheaf and bounded delays in communication and computation, nonlinear sheaf diffusion converges to a minimizer of the Dirichlet energy of the coordination sheaf at a linear rate proportional to the delay bound. We further show that this linear convergence is attained from arbitrary initial conditions and the analysis depends on the spectrum of the sheaf Laplacian in a manner that generalizes the standard graph Laplacian case. We provide several numerical simulations to validate our theoretical results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_00270 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asynchronous Nonlinear Sheaf Diffusion for Multi-Agent Coordination Zhao, Yichen Hanks, Tyler Riess, Hans Cohen, Samuel Hale, Matthew Fairbanks, James Optimization and Control Systems and Control 93A16 (Primary), 55N30, 05C50 (Secondary) Cellular sheaves and sheaf Laplacians provide a far-reaching generalization of graphs and graph Laplacians, resulting in a wide array of applications ranging from machine learning to multi-agent control. In the context of multi-agent systems, so called coordination sheaves provide a unifying formalism that models heterogeneous agents and coordination goals over undirected communication topologies, and applying sheaf diffusion drives agents to achieve their coordination goals. Existing literature on sheaf diffusion assumes that agents can communicate and compute updates synchronously, which is an unrealistic assumption in many scenarios where communication delays or heterogeneous agents with different compute capabilities cause disagreement among agents. To address these challenges, we introduce asynchronous nonlinear sheaf diffusion. Specifically, we show that under mild assumptions on the coordination sheaf and bounded delays in communication and computation, nonlinear sheaf diffusion converges to a minimizer of the Dirichlet energy of the coordination sheaf at a linear rate proportional to the delay bound. We further show that this linear convergence is attained from arbitrary initial conditions and the analysis depends on the spectrum of the sheaf Laplacian in a manner that generalizes the standard graph Laplacian case. We provide several numerical simulations to validate our theoretical results. |
| title | Asynchronous Nonlinear Sheaf Diffusion for Multi-Agent Coordination |
| topic | Optimization and Control Systems and Control 93A16 (Primary), 55N30, 05C50 (Secondary) |
| url | https://arxiv.org/abs/2510.00270 |