Regularising the primal formulation of optimal transport (OT) with a strictly convex term leads to enhanced numerical complexity and a denser transport plan. Many formulations impose a global constraint on the transport plan, for instance by relying on entropic regularisation. As it is more expensive to diffuse mass for outlier points compared to central ones, this typically results in a significant imbalance in the way mass is spread across the points. This can be detrimental for some applications where a minimum of smoothing is required per point. To remedy this, we introduce OT with Adaptive RegularIsation (OTARI), a new formulation of OT that imposes constraints on the mass going in or/and out of each point. We then showcase the benefits of this approach for domain adaptation.

翻译：对最优传输（OT）原始形式施加严格凸项的正则化，能够提升数值计算复杂度并获得更密集的传输方案。许多现有方法通过依赖熵正则化等方式对传输方案施加全局约束。由于离群点与中心点相比需要更高代价进行质量扩散，这通常会导致质量在各点间分布出现显著不均衡。对于某些要求各点保持最小平滑度的应用场景，这种特性可能产生不利影响。为解决该问题，我们提出自适应正则化最优传输（OTARI）——一种对每个点的输入/输出质量施加约束的新型OT形式。最后，我们展示了该方法在领域自适应任务中的优势。