Theoretically Grounded Loss Functions and Algorithms for Efficient Multi-Class Abstention

The authors introduce new families of surrogate losses for the multi-class abstention loss function, including state-of-the-art surrogate losses in the single-stage setting and a novel family of loss functions in the two-stage setting. They prove strong non-asymptotic and hypothesis set-specific consistency guarantees for these surrogate losses, which upper-bound the estimation error of the abstention loss function in terms of the estimation error of the surrogate loss.