# Information-Theoretic Equivalence of Entropic Multi-Marginal Optimal Transport: A Theory for Multi-Agent Communication

arXiv: https://arxiv.org/abs/2208.10256 · HTML: https://mlsanity.com/paper/2208.10256/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 51 references that are in the map.
- First posted on arXiv 22 Aug 2022.

## Builds on (most cited first, 18 of 18)

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- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Cooperative Inverse Reinforcement Learning](https://mlsanity.com/paper/1606.03137/) (2016)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [Deep Learning Enabled Semantic Communication Systems](https://mlsanity.com/paper/2006.10685/) (2020)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [Multi-Game Decision Transformers](https://mlsanity.com/paper/2205.15241/) (2022)
- [6G Networks: Beyond Shannon Towards Semantic and Goal-Oriented Communications](https://mlsanity.com/paper/2011.14844/) (2020)
- [Semantics-Empowered Communication for Networked Intelligent Systems](https://mlsanity.com/paper/2007.11579/) (2020)
- [What is Semantic Communication? A View on Conveying Meaning in the Era of Machine Intelligence](https://mlsanity.com/paper/2110.00196/) (2021)
- [Policy Optimization as Wasserstein Gradient Flows](https://mlsanity.com/paper/1808.03030/) (2018)
- [A mathematical theory of cooperative communication](https://mlsanity.com/paper/1910.02822/) (2019)
- [Multi-marginal optimal transport and probabilistic graphical models](https://mlsanity.com/paper/2006.14113/) (2020)
- [Information Constrained Optimal Transport: From Talagrand, to Marton, to Cover](https://mlsanity.com/paper/2008.10249/) (2020)
- [Optimal Cooperative Inference](https://mlsanity.com/paper/1705.08971/) (2017)
- [Generalizing the theory of cooperative inference](https://mlsanity.com/paper/1810.02423/) (2018)
- [Generalized Talagrand Inequality for Sinkhorn Distance using Entropy Power Inequality](https://mlsanity.com/paper/2109.08430/) (2021)

## Abstract (arXiv)

In this paper, we propose our information-theoretic equivalence of entropic multi-marginal optimal transport (MOT). This equivalence can be easily reduced to the case of entropic optimal transport (OT). Because OT is widely used to compare differences between knowledge or beliefs, we apply this result to the communication between agents with different beliefs. Our results formally prove the statement that entropic OT is information-theoretically optimal given by Wang et al. [2020] and generalize it to the multi-agent case. We believe that our work can shed light on OT theory in future multi-agent teaming systems.