We study the key framework of learning with abstention in the multi-class
classification setting. In this setting, the learner can choose to abstain from
making a prediction with some pre-defined cost. We present a series of new
theoretical and algorithmic results for this learning problem in the
predictor-rejector framework. We introduce several new families of surrogate
losses for which we prove strong non-asymptotic and hypothesis set-specific
consistency guarantees, thereby resolving positively two existing open
questions. These guarantees provide upper bounds on the estimation error of the
abstention loss function in terms of that of the surrogate loss. We analyze
both a single-stage setting where the predictor and rejector are learned
simultaneously and a two-stage setting crucial in applications, where the
predictor is learned in a first stage using a standard surrogate loss such as
cross-entropy. These guarantees suggest new multi-class abstention algorithms
based on minimizing these surrogate losses. We also report the results of
extensive experiments comparing these algorithms to the current
state-of-the-art algorithms on CIFAR-10, CIFAR-100 and SVHN datasets. Our
results demonstrate empirically the benefit of our new surrogate losses and
show the remarkable performance of our broadly applicable two-stage abstention
algorithm.

我们研究了多类别分类中的学习与弃权的关键框架，介绍了一系列新的理论和算法结果，提出了几个新的代理损失函数家族，并分析了单阶段和两阶段学习设置的保证和应用，证明了我们的代理损失的优越性，并展示了广泛适用的两阶段弃权算法的卓越性能。

预测者 - 排斥者多类弃权：理论分析与算法

Predictor-Rejector Multi-Class Abstention: Theoretical Analysis and  Algorithms

Learning with abstention is a key scenario where the learner can abstain from
making a prediction at some cost. In this paper, we analyze the score-based
formulation of learning with abstention in the multi-class classification
setting. We introduce new families of surrogate losses for the abstention loss
function, which include the state-of-the-art surrogate losses in the
single-stage setting and a novel family of loss functions in the two-stage
setting. We 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. Our bounds can help compare different score-based surrogates
and guide the design of novel abstention algorithms by minimizing the proposed
surrogate losses. We experimentally evaluate our new algorithms on CIFAR-10,
CIFAR-100, and SVHN datasets and the practical significance of our new
surrogate losses and two-stage abstention algorithms. Our results also show
that the relative performance of the state-of-the-art score-based surrogate
losses can vary across datasets.

通过引入新的代理损失函数，分析了多类别分类中学习与弃权的打分式公式，证明了这些代理损失函数的非渐近性和假设集特定一致性保证上界了弃权损失函数的估计误差，实验评估了新算法在几个数据集上的效果并展示了阶段性弃权算法的实际重要性。