In this video at 43:00, a version of the PAC bound for generalization error $\epsilon$, which I hadn't seen before, is quoted:
$$\epsilon^2 < \frac{\log{|H_\epsilon|} + \log{1/\delta}}{2m}$$
where $m$ is the number of samples, $\delta$ is the confidence parameter, and $H_\epsilon$ is the cardinality of an "$\epsilon$-cover of the hypothesis class", where he defines an $\epsilon$-cover as a set of subsets of the hypothesis class, such that the probability that two hypothesis in the same subset disagree is less than $\epsilon$.
Apart from the fact that this isn't a formal statement, I couldn't prove this myself. Has anyone heard of this version of PAC, and if so, could they point me to resources explaining it, or give some explanation here?