We introduce a novel framework of ranking with abstention, where the learner
can abstain from making prediction at some limited cost $c$. We present a
extensive theoretical analysis of this framework including a series of
$H$-consistency bounds for both the family of linear functions and that of
neural networks with one hidden-layer. These theoretical guarantees are the
state-of-the-art consistency guarantees in the literature, which are upper
bounds on the target loss estimation error of a predictor in a hypothesis set
$H$, expressed in terms of the surrogate loss estimation error of that
predictor. We further argue that our proposed abstention methods are important
when using common equicontinuous hypothesis sets in practice. We report the
results of experiments illustrating the effectiveness of ranking with
abstention.

我们介绍了一种新的排名框架，其中学习器可以以有限的代价 $c$ 放弃对某些预测的判断，并对这个框架进行了广泛的理论分析，包括一系列 $f$- 一致性边界，达到了此领域的最新理论保证水平，我们进一步提出，这种新的放弃策略在使用常见的等连续假设空间时显得尤为重要，我们还报告了实验结果，证明了带放弃策略的排名方法的有效性。