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Decentralized Entropic Optimal Transport for Distributed Distribution Comparison by Wang, Xiangfeng; Xu, Hongteng; Yang, Moyi is a scholarly article available to read on EtoBox.

What is Decentralized Entropic Optimal Transport for Distributed Distribution Comparison about?

Distributed distribution comparison aims to measure the distance between the distributions whose data are scattered across different agents in a distributed system and cannot even be shared directly among the agents. In this study, we propose a novel decentralized entropic optimal transport (DEOT) method, which provides a communication-efficient and privacy-preserving solution to this problem with theoretical guarantees. In particular, we design a mini-batch randomized block-coordinate descent (MRBCD) scheme to optimize the DEOT distance in its dual form. The dual variables are scattered across different agents and updated locally and iteratively with limited communications among partial agents. The kernel matrix involved in the gradients of the dual variables is estimated by a decentralized kernel approximation method, in which each agent only needs to approximate and store a sub-kernel matrix by one-shot communication and without sharing raw data. Besides computing entropic Wasserstein distance, we show that the proposed MRBCD scheme and kernel approximation method also apply to entropic Gromov-Wasserstein distance. We analyze our method's communication complexity and, under mild

Author

Wang, Xiangfeng; Xu, Hongteng; Yang, Moyi

Published

2023

Language

EN