Fast and Provably Convergent Algorithms for Gromov-Wasserstein in Graph Learning

In this paper, we study the design and analysis of a class of efficient algorithms for computing the Gromov-Wasserstein (GW) distance tailored to large-scale graph learning tasks. Armed with the Luo-Tseng error bound condition~\cite{luo1992error}, two proposed algorithms, called Bregman Alternating Projected Gradient (BAPG) and hybrid Bregman Proximal Gradient (hBPG) are proven to be (linearly) convergent. Upon task-specific properties, our analysis further provides novel theoretical insights to guide how to select the best fit method. As a result, we are able to provide comprehensive experiments to validate the effectiveness of our methods on a host of tasks, including graph alignment, graph partition, and shape matching. In terms of both wall-clock time and modeling performance, the proposed methods achieve state-of-the-art results.