  We study crowdsourced PAC learning of threshold functions, where the labels
are gathered from a pool of annotators some of whom may behave adversarially.
This is yet a challenging problem and until recently has computationally and
query efficient PAC learning algorithm been established by Awasthi et al.
(2017). In this paper, we show that by leveraging the more easily acquired
pairwise comparison queries, it is possible to exponentially reduce the label
complexity while retaining the overall query complexity and runtime. Our main
algorithmic contributions are a comparison-equipped labeling scheme that can
faithfully recover the true labels of a small set of instances, and a
label-efficient filtering process that in conjunction with the small labeled
set can reliably infer the true labels of a large instance set.
