Goldwasser et al. (2021) recently proposed the setting of PAC verification, where a hypothesis (machine learning model) that purportedly satisfies the agnostic PAC learning objective is verified using an interactive proof. In this paper we develop this notion further in a number of ways. First, we prove a lower bound of $\Omega\left(\sqrt{d}/\varepsilon^2\right)$ i.i.d.\ samples for PAC verification of hypothesis classes of VC dimension $d$. Second, we present a protocol for PAC verification of unions of intervals over $\mathbb{R}$ that improves upon their proposed protocol for that task, and matches our lower bound's dependence on $d$. Third, we introduce a natural generalization of their definition to verification of general statistical algorithms, which is applicable to a wider variety of settings beyond agnostic PAC learning. Showcasing our proposed definition, our final result is a protocol for the verification of statistical query algorithms that satisfy a combinatorial constraint on their queries.

翻译：Goldwasser等人(2021)近期提出了PAC验证的设置，其中声称满足不可知PAC学习目标的假设（机器学习模型）通过交互式证明进行验证。本文从多个方面进一步发展了这一概念。首先，我们证明了对于VC维度为$d$的假设类，PAC验证需要$\Omega\left(\sqrt{d}/\varepsilon^2\right)$个独立同分布样本的下界。其次，我们提出了$\mathbb{R}$上区间并集PAC验证的协议，该协议改进了他们针对该任务提出的协议，并与我们下界中关于$d$的依赖关系相匹配。第三，我们将其定义自然地推广到一般统计算法的验证，该定义适用于除不可知PAC学习之外的更广泛场景。为展示我们提出的定义，最后的结果是一个验证满足查询组合约束的统计查询算法的协议。