Fast and Scalable Multi-Agent Distribution Matching via Partitioned Optimal Transport

Abstract:This paper presents a scalable optimal-transport-based framework for terminal distribution matching in multi-agent systems. While optimal transport provides a natural way to measure distributional mismatch and assign agents to a desired spatial distribution, global discrete transport can become computationally expensive for large-scale systems. We address this bottleneck by partitioning agents and target samples into spatially corresponding blocks and solving smaller local transport problems. Under a mass-balance condition, the resulting restricted coupling remains feasible for the global problem and provides an upper bound on the Wasserstein cost. The local assignments generate target locations for finite-horizon agent control, applicable to both linear and nonlinear dynamics. By alternating local assignment and control, we establish a cycle-to-cycle descent guarantee for the resulting transport surrogate. The proposed framework therefore enables scalable terminal distribution matching while retaining a rigorous connection to the Wasserstein objective. The technical soundness of the proposed results is validated through simulations.

Multiagent Systems (cs.MA); Robotics (cs.RO); Systems and Control (eess.SY); Optimization and Control (math.OC)

arXiv:2609.38960 [cs.MA]

(or arXiv:2609.38960v1 [cs.MA] for this version)

https://doi.org/10.48550/arXiv.2609.38960 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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