# Information Constrained Optimal Transport: From Talagrand, to Marton, to Cover

arXiv: https://arxiv.org/abs/2008.10249 · HTML: https://mlsanity.com/paper/2008.10249/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Aug 2020.

## Built on by (most cited first, 8 of 8)

- [Sinkhorn Distributionally Robust Optimization](https://mlsanity.com/paper/2109.11926/) (2021)
- [InfoOT: Information Maximizing Optimal Transport](https://mlsanity.com/paper/2210.03164/) (2022)
- [Gaussian Rate-Distortion-Perception Coding and Entropy-Constrained Scalar Quantization](https://mlsanity.com/paper/2409.02388/) (2024)
- [Generalized Talagrand Inequality for Sinkhorn Distance using Entropy Power Inequality](https://mlsanity.com/paper/2109.08430/) (2021)
- [Information Geometry for the Working Information Theorist](https://mlsanity.com/paper/2310.03884/) (2023)
- [Characterization of the Distortion-Perception Tradeoff for Finite Channels with Arbitrary Metrics](https://mlsanity.com/paper/2402.02265/) (2024)
- [Information-Theoretic Equivalence of Entropic Multi-Marginal Optimal Transport: A Theory for Multi-Agent Communication](https://mlsanity.com/paper/2208.10256/) (2022)
- [Two-Sided Bounds for Entropic Optimal Transport via a Rate-Distortion Integral](https://mlsanity.com/paper/2604.14061/) (2026)

## Abstract (arXiv)

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.