Gromov Wasserstein (GW) distance is a powerful tool for comparing and aligning probability distributions supported on different metric spaces. It has become the main modeling technique for aligning heterogeneous data for a wide range of graph learning tasks. However, the GW distance is known to be highly sensitive to outliers, which can result in large inaccuracies if the outliers are given the same weight as other samples in the objective function. To mitigate this issue, we introduce a new and robust version of the GW distance called RGW. RGW features optimistically perturbed marginal constraints within a $\varphi$-divergence based ambiguity set. To make the benefits of RGW more accessible in practice, we develop a computationally efficient algorithm, Bregman proximal alternating linearization minimization, with a theoretical convergence guarantee. Through extensive experimentation, we validate our theoretical results and demonstrate the effectiveness of RGW on real-world graph learning tasks, such as subgraph matching and partial shape correspondence.

翻译：Gromov Wasserstein（GW）距离是比较和对齐不同度量空间上概率分布的有力工具，已成为对齐异构数据以支持广泛图学习任务的主流建模技术。然而，GW距离对离群点高度敏感，若这些离群点在目标函数中被赋予与其他样本相同的权重，将导致较大的不准确性。为解决此问题，我们提出一种名为RGW的新的鲁棒性GW距离。RGW在基于$\varphi$-散度的模糊集合内采用乐观扰动的边际约束。为使RGW的优势更易在实际中应用，我们开发了一种计算高效的算法——Bregman近端交替线性化最小化，并具有理论收敛性保证。通过大量实验，我们验证了理论结果，并展示了RGW在真实图学习任务（如子图匹配和部分形状对应）中的有效性。