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，在可实现和不可知设定下，布尔函数的量子批量学习的样本复杂度在形式和阶数上与相应的经典样本复杂度相同。本文将此看似令人惊讶的结论拓展至批量多类别学习、在线布尔学习以及在线多类别学习。针对在线学习结果，我们首先考虑Dawid和Tewari（2022）经典模型的自适应对抗变体。随后，我们引入（据我们所知）首个基于量子样本的在线学习模型。