Optimal Transport-Based Decentralized Multi-Agent Distribution Matching

2026-01-02

arXiv.org

AI Summary

This work addresses the problem of coordinating decentralized multi-agent systems to achieve a prescribed terminal spatial distribution. Building upon optimal transport theory, the authors propose a fully decentralized control framework that relies solely on local information. By introducing locally computable approximations of the Wasserstein distance, sequential weight updates, and a memory-based correction mechanism, the global distribution-matching objective is effectively decomposed into individual decision-making processes. The approach is applicable to both linear and nonlinear agent dynamics and comes with formal convergence guarantees, making it particularly suitable for communication-constrained environments. Simulation results demonstrate that the proposed method achieves high efficiency, scalability, and robustness under fully decentralized conditions, significantly improving distribution-matching performance in multi-agent systems.

Technology Category

• Multiagent Systems: Distributed Problem Solving
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Decentralized Web and Fediverse systems
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

This paper presents a decentralized control framework for distribution matching in multi-agent systems (MAS), where agents collectively achieve a prescribed terminal spatial distribution. The problem is formulated using optimal transport (Wasserstein distance), which provides a principled measure of distributional discrepancy and serves as the basis for the control design. To avoid solving the global optimal transport problem directly, the distribution-matching objective is reformulated into a tractable per-agent decision process, enabling each agent to identify its desired terminal locations using only locally available information. A sequential weight-update rule is introduced to construct feasible local transport plans, and a memory-based correction mechanism is incorporated to maintain reliable operation under intermittent and range-limited communication. Convergence guarantees are established, showing cycle-wise improvement of a surrogate transport cost under both linear and nonlinear agent dynamics. Simulation results demonstrate that the proposed framework achieves effective and scalable distribution matching while operating fully in a decentralized manner.

Problem

• multi-agent systems
• distribution matching
• optimal transport
• decentralized control
• Wasserstein distance

Innovation

• Optimal Transport
• Decentralized Control
• Multi-Agent Systems
• Wasserstein Distance
• Distribution Matching