Arunachalam and de Wolf (2018) showed that the sample complexity of quantum batch learning of boolean functions, in the realizable and agnostic settings, has the same form and order as the corresponding classical sample complexities. In this paper, we extend this, ostensibly surprising, message to batch multiclass learning, online boolean learning, and online multiclass learning. For our online learning results, we first consider an adaptive adversary variant of the classical model of Dawid and Tewari (2022). Then, we introduce the first (to the best of our knowledge) model of online learning with quantum examples.

翻译：Arunachalam和de Wolf（2018）证明了在可实现与不可知设置下，布尔函数量子批处理学习的样本复杂度与经典样本复杂度具有相同的形式和量级。本文将该看似意外的结论拓展至批处理多类学习、在线布尔学习及在线多类学习。针对在线学习结果，我们首先考虑了Dawid与Tewari（2022）经典模型的自适应对抗变体，随后引入了据我们所知的第一个量子样本在线学习模型。