A Two-Stage Learning-to-Defer Approach for Multi-Task Learning

The Two-Stage Learning-to-Defer (L2D) framework has been extensively studied for classification and, more recently, regression tasks. However, many real-world applications require solving both tasks jointly in a multi-task setting. We introduce a novel Two-Stage L2D framework for multi-task learning that integrates classification and regression through a unified deferral mechanism. Our method leverages a two-stage surrogate loss family, which we prove to be both Bayes-consistent and $(\mathcal{G}, \mathcal{R})$-consistent, ensuring convergence to the Bayes-optimal rejector. We derive explicit consistency bounds tied to the cross-entropy surrogate and the $L_1$-norm of agent-specific costs, and extend minimizability gap analysis to the multi-expert two-stage regime. We also make explicit how shared representation learning -- commonly used in multi-task models -- affects these consistency guarantees. Experiments on object detection and electronic health record analysis demonstrate the effectiveness of our approach and highlight the limitations of existing L2D methods in multi-task scenarios.