We study the problem of {\em crowdsourced PAC learning} of Boolean-valued functions through enriched queries, a problem that has attracted a surge of recent research interests. In particular, we consider that the learner may query the crowd to obtain a label of a given instance or a comparison tag of a pair of instances. This is a challenging problem and only recently have budget-efficient algorithms been established for the scenario where the majority of the crowd are correct. In this work, we investigate the significantly more challenging case that the majority are incorrect which renders learning impossible in general. 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 learn the underlying function while the labeling cost is significantly mitigated by the enriched and more easily obtained queries.

中文翻译：

---

通过成对比较从人群中进行半验证学习

我们通过丰富的查询来研究布尔值函数的 {\em 众包 PAC 学习}问题，这个问题最近引起了大量研究兴趣。特别地，我们认为学习器可以查询人群以获得给定实例的标签或一对实例的比较标签。这是一个具有挑战性的问题，直到最近才为大多数人群正确的场景建立了预算有效的算法。在这项工作中，我们调查了更具挑战性的情况，即大多数人是不正确的，这使得学习通常是不可能的。我们表明，在 Charikar~et~al.~(2017) 的 {semi-verified model} 下，我们可以（有限地）访问一个总是返回正确注释的可信预言机，