In this work we hope to combine the work from the robust optimization literature anddeep learning literature to create a general framework for robust matching. It can be usedto enhance performance in existing deep learning frameworks or to improve performancein robust learning frameworks. We leverage the aforementioned primal-dual trainingtechniques to learn more robust matching estimators. We formulate a Lagrangian primal-dual training framework for robust matching problems in asemi-supervised setting. Synthetic experiments have proved promising in a semi-supervised setting, and tests are underway for real-world data.