Problem
Research questions and friction points this paper is trying to address.
multi-agent systems
distribution matching
optimal transport
scalability
Wasserstein distance
Fast and Scalable Multi-Agent Distribution Matching via Partitioned Optimal Transport
🤖 AI Summary
This study addresses the high computational cost and inefficiency of global optimal transport in large-scale multi-agent systems for terminal distribution matching. We propose a scalable framework based on partitioned optimal transport that divides agents and target samples into spatial blocks to solve local transport problems, alternating with finite-horizon control to achieve global matching. Under mass balance conditions, we establish the global feasibility of locally coupled solutions, derive an upper bound on the Wasserstein cost, and guarantee cyclic descent convergence. By integrating optimal transport, spatial partitioning, and dynamical control theory, this work achieves scalable terminal distribution matching while rigorously preserving the Wasserstein optimization objective. Simulation results validate the effectiveness of the proposed approach.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Optimal Transport
Multi-Agent Systems
Distribution Matching
Scalability
Wasserstein Distance
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