论文标题
Monge-Kantorovich通过收缩和流量限制的最佳运输
Monge-Kantorovich Optimal Transport Through Constrictions and Flow-rate Constraints
论文作者
论文摘要
我们考虑到运输资源/质量的问题，同时通过沿着指定终端分布之间的路径限制限制流程。收缩在指定点被概念化为通行站，限制了跨越流速。我们通过限制了质量元素交叉收费站的概率密度来量化流量率约束，并在形式主义的Kantorovich型中施放了运输计划。我们的团队最近的工作着重于Monge Maps的存在，以最大程度地减少平均动能的限制运输。本文目前的表述除了基本上更一般性外，还被视为（广义的）多核心运输问题，这是对现代机器学习文献引起的极大兴趣的问题，并激发了广泛的计算分析。我们形式主义的一个促成特征是表示传输速度的平均二次成本作为涉及跨越时间的凸约束。
We consider the problem to transport resources/mass while abiding by constraints on the flow through constrictions along their path between specified terminal distributions. Constrictions, conceptualized as toll stations at specified points, limit the flow rate across. We quantify flow-rate constraints via a bound on a sought probability density of the times that mass-elements cross toll stations and cast the transportation scheduling in a Kantorovich-type of formalism. Recent work by our team focused on the existence of Monge maps for similarly constrained transport minimizing average kinetic energy. The present formulation in this paper, besides being substantially more general, is cast as a (generalized) multi-marginal transport problem - a problem of considerable interest in modern-day machine learning literature and motivated extensive computational analyses. An enabling feature of our formalism is the representation of an average quadratic cost on the speed of transport as a convex constraint that involves crossing times.
