Gromov–Wasserstein distances: Entropic regularization, duality and sample complexity
Gromov–Wasserstein距离：熵正则化、对偶与样本复杂度
The Gromov–Wasserstein (GW) distance, rooted in optimal transport (OT) theory, quantifies dissimilarity between metric measure spaces and provides a framework for aligning heterogeneous datasets. While computational aspects of the GW problem have been widely studied, a duality theory and fundamental statistical questions concerning empirical convergence rates remained obscure. This work closes these gaps for the quadratic GW distance over Euclidean spaces of different…