What is the Right Notion of Distance between Predict-then-Optimize Tasks?

Optimal transport-based dataset distances are a principled way to measure task similarity, informing tasks like domain adaptation and transfer learning, typically assessed by prediction error minimization. However, in Predict-then-Optimize (PtO) frameworks, success is measured by decision regret minimization. We show that feature- and label-based distances lack informativeness in PtO and propose a new decision-aware distance that effectively captures adaptation success in PtO.