PAC Verification of Statistical Algorithms
This work addresses the verification of statistical algorithms for researchers in theoretical machine learning, offering incremental advances in sample complexity and protocol design.
The paper tackles the problem of verifying machine learning models and statistical algorithms by establishing a sample complexity lower bound for PAC verification and proposing improved protocols for specific tasks, achieving a protocol for unions of intervals that matches the lower bound's dependence on VC dimension.
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 $Ω\left(\sqrt{d}/\varepsilon^2\right)$ 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.