论文标题
信息限制的最佳运输：从Talagrand，到Marton，覆盖
Information Constrained Optimal Transport: From Talagrand, to Marton, to Cover
论文作者
论文摘要
最佳运输问题研究如何以最具成本效益的方式将一种措施运输到另一种措施，并具有从经济学到机器学习的广泛应用。在本文中，我们介绍并研究了该问题的信息限制。我们的研究得出了塔格兰（Talagrand）著名的运输成本不平等的加强和概括。按照Marton的方法，我们表明，新的运输成本不平等可用于恢复旧和新的量度结果。最后，我们将这种新不平等的应用程序应用于网络信息理论。我们表明，它可用于几乎立即恢复最新的解决方案，以解决有关继电器渠道容量的长期开放问题。
The optimal transport problem studies how to transport one measure to another in the most cost-effective way and has wide range of applications from economics to machine learning. In this paper, we introduce and study an information constrained variation of this problem. Our study yields a strengthening and generalization of Talagrand's celebrated transportation cost inequality. Following Marton's approach, we show that the new transportation cost inequality can be used to recover old and new concentration of measure results. Finally, we provide an application of this new inequality to network information theory. We show that it can be used to recover almost immediately a recent solution to a long-standing open problem posed by Cover regarding the capacity of the relay channel.
