We show a generic reduction from multiclass differentially private PAC learning to binary private PAC learning. We apply this transformation to a recently proposed binary private PAC learner to obtain a private multiclass learner with sample complexity that has a polynomial dependence on the multiclass Littlestone dimension and a poly-logarithmic dependence on the number of classes. This yields an exponential improvement in the dependence on both parameters over learners from previous work. Our proof extends the notion of $\Psi$-dimension defined in work of Ben-David et al. [JCSS '95] to the online setting and explores its general properties.

翻译：我们展示了从多级的私人PAC学习到二进制私人PAC学习的普遍程度的下降。我们将这一转变应用到最近提议的二进制私人PAC学习者,以获得一个具有样本复杂性、对多级Littlestone维度具有多级依赖性和对班数具有多级依赖性的私营多级学习者。这导致对两个参数的依赖比以往学习者更加指数化。我们的证据将Ben-David等人的工作所确定的$\Psi$-dimenion概念[JCSS'95]延伸至在线设置,并探索其一般属性。