Semi-verified PAC Learning from the Crowd with Pairwise Comparisons

We study the problem of crowdsourced PAC learning of threshold functions with pairwise comparisons. This is a challenging problem and only recently have query-efficient algorithms been established in the scenario where the majority of the crowd are perfect. In this work, we investigate the significantly more challenging case that the majority are incorrect, which in general renders learning impossible. We show that under the semi-verified model of Charikar~et~al.~(2017), where we have (limited) access to a trusted oracle who always returns the correct annotation, it is possible to PAC learn the underlying hypothesis class while drastically mitigating the labeling cost via the more easily obtained comparison queries. Orthogonal to recent developments in semi-verified or list-decodable learning that crucially rely on data distributional assumptions, our PAC guarantee holds by exploring the wisdom of the crowd.