[henry2015]

Thanks for your quick reply Professor!

Now, I wonder why "we cannot just plug in g for h in the Hoeffding inequality". Given g is one of h's and for each h, Hoeffding inequality is valid for the upper bound of P[|Ein(h) - Eout(h)| > E]. Even g is picked after we look at all the outputs of all h's, g is still one of h's. So Hoeffding inequality should be still valid for g. No?

Thanks!