基于分区最优传输的快速可扩展多智能体分布匹配

中文摘要 AI 辅助

本文提出了一种基于最优传输的可扩展框架，用于多智能体系统中的终端分布匹配。虽然最优传输为衡量分布失配并将智能体分配到期望的空间分布提供了一种自然的方法，但对于大规模系统，全局离散传输在计算上可能变得昂贵。我们通过将智能体和目标样本划分为空间对应的区块，并求解较小的局部传输问题来解决这一瓶颈。在质量平衡条件下，所得的受限耦合对全局问题仍然可行，并为Wasserstein代价提供了上界。局部分配为有限时域智能体控制生成目标位置，适用于线性和非线性动力学。通过交替进行局部分配和控制，我们为所得的传输替代目标建立了循环间下降保证。因此，所提出的框架能够在保持与Wasserstein目标严格联系的同时，实现可扩展的终端分布匹配。通过仿真验证了所提出结果的技术可靠性。

英文摘要

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.

发表机构

• Texas Tech University（德克萨斯理工大学）

机构由 AI 辅助整理，请以论文原文为准。