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

The Two-Stage Learning-to-Defer framework has been extensively studied for classification and, more recently, regression tasks. However, many contemporary applications involve both classification and regression in an interdependent manner. In this work, we introduce a novel Two-Stage Learning-to-Defer framework for multi-task learning that jointly addresses these tasks. Our approach leverages a two-stage surrogate loss family, which we prove to be both ($\mathcal{G}, \mathcal{R}$)-consistent and Bayes-consistent, providing strong theoretical guarantees of convergence to the Bayes-optimal rejector. We establish consistency bounds explicitly linked to the cross-entropy surrogate family and the $L_1$-norm of the agents' costs, extending the theoretical minimizability gap analysis to the two-stage setting with multiple experts. We validate our framework on two challenging tasks: object detection, where classification and regression are tightly coupled, and existing methods fail, and electronic health record analysis, in which we highlight the suboptimality of current learning-to-defer approaches.