When No-Rejection Learning is Consistent for Regression with Rejection

TL;DR

This paper investigates a no-rejection learning approach for regression with rejection, establishing its consistency and providing bounds on excess risk, supported by empirical evidence, to improve human-AI prediction systems.

Contribution

It introduces and analyzes a no-rejection learning strategy for regression with rejection, proving its consistency and bounding excess risk without relying on weak realizability.

Findings

The no-rejection strategy is consistent under weak realizability.

Excess risk can be bounded by prediction and calibration errors.

Empirical results demonstrate the effectiveness of the proposed approach.

Abstract

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.