|Information Constrained Optimal Transport: From Talagrand, to Marton, to Cover
|Yikun Bai, Xiugang Wu, University of Delaware, United States; Ayfer Ozgur, Stanford University, United States
|S.8: Information Inequalities
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|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 our new transportation cost inequality can be used to recover old and new concentration of measure results. Finally, we provide an application of our transportation cost inequality in network information theory. We show that it can be used to recover a recent solution to a long-standing open problem posed by Cover regarding the capacity of the relay channel.