Given a collection of probability measures, a practitioner sometimes needs to
find an "average" distribution which adequately aggregates reference
distributions. A theoretically appealing notion of such an average is the
Wasserstein barycenter, which is the primal focus of our work. By building upon
the dual formulation of Optimal Transport (OT), we propose a new scalable
approach for solving the Wasserstein barycenter problem. Our methodology is
based on the recent Neural OT solver: it has bi-level adversarial learning
objective and works for general cost functions. These are key advantages of our
method, since the typical adversarial algorithms leveraging barycenter tasks
utilize tri-level optimization and focus mostly on quadratic cost. We also
establish theoretical error bounds for our proposed approach and showcase its
applicability and effectiveness on illustrative scenarios and image data
setups.

使用建立在最优输运（Optimal Transport）的对偶形式基础上的新的可扩展方法，提出了求解 Wasserstein barycenter 问题的策略，具有双层对抗学习目标且适用于广义成本函数，同时在理论上建立了误差界限，并在图像数据集构建和举例场景中展示了其适用性和有效性。