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

TL;DR

This paper establishes an information-theoretic equivalence for entropic multi-marginal optimal transport, extending its application to multi-agent communication and belief comparison, and generalizing prior optimality results.

Contribution

It introduces a formal equivalence for entropic multi-marginal optimal transport and applies it to multi-agent belief communication, expanding OT theory.

Findings

Proves entropic OT is information-theoretically optimal.

Generalizes OT optimality to multi-agent systems.

Provides a theoretical foundation for multi-agent communication using OT.

Abstract

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.