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Learning with abstention is a key scenario where the learner can abstain frommaking a prediction at some cost. In this paper, we analyze the score-basedformulation of learning with abstention in the multi-class classificationsetting. We introduce new families of surrogate losses for the abstention lossfunction, which include the state-of-the-art surrogate losses in thesingle-stage setting and a novel family of loss functions in the two-stagesetting. We prove strong non-asymptotic and hypothesis set-specific consistencyguarantees for these surrogate losses, which upper-bound the estimation errorof the abstention loss function in terms of the estimation error of thesurrogate loss. Our bounds can help compare different score-based surrogatesand guide the design of novel abstention algorithms by minimizing the proposedsurrogate losses. We experimentally evaluate our new algorithms on CIFAR-10,CIFAR-100, and SVHN datasets and the practical significance of our newsurrogate losses and two-stage abstention algorithms. Our results also showthat the relative performance of the state-of-the-art score-based surrogatelosses can vary across datasets.

Theoretically Grounded Loss Functions and Algorithms for Score-Based Multi-Class Abstention