[henry2015]

What the book states "e cannot just plug in g for h in the Hoeffding inequality" means that Hoeffding inequality is still true for g as it is one of the h's. But Hoeffding inequality seems failed for g because we are cherry picking.

Just like flipping an unbiased coin 1 million times, we should see 500K heads and 500K tails, but we might have "bad luck" that we see 1 million heads but the P(head) is still 0.5.

Do I interpret correctly?

Thanks a lot!