When No-Rejection Learning is Consistent for Regression with Rejection
This work addresses a gap in consistent learning methods for regression with rejection, which is important for improving human-AI interaction in prediction tasks, though it is incremental as it builds on prior classification-focused research.
The paper tackles the regression with rejection problem by proposing a no-rejection learning strategy that uses all data to learn the predictor, establishing its consistency under weak realizability and bounding excessive risk otherwise, with empirical evidence showing its advantage.
Learning with rejection has been a prototypical model for studying the human-AI interaction on prediction tasks. Upon the arrival of a sample instance, the model first uses a rejector to decide whether to accept and use the AI predictor to make a prediction or reject and defer the sample to humans. Learning such a model changes the structure of the original loss function and often results in undesirable non-convexity and inconsistency issues. For the classification with rejection problem, several works develop consistent surrogate losses for the joint learning of the predictor and the rejector, while there have been fewer works for the regression counterpart. This paper studies the regression with rejection (RwR) problem and investigates a no-rejection learning strategy that uses all the data to learn the predictor. We first establish the consistency for such a strategy under the weak realizability condition. Then for the case without the weak realizability, we show that the excessive risk can also be upper bounded with the sum of two parts: prediction error and calibration error. Lastly, we demonstrate the advantage of such a proposed learning strategy with empirical evidence.