# Covering numbers to show that H is agnostically PAC-learnable

Suppose $$X=[0,1]$$ and $$Y=[0,1]$$, and we use the squared loss

Let's define the hypothesis class $$H = {h(x) = (x-a)^2 : a \in [0,1]}$$.

Question: How can covering numbers be used to show that this class is agnostically PAC-learnable, and prove an upper bound on $$|L_S(h) - L_D(h)|$$, which holds simultaneously for all $$h\in H$$ with probability at least $$1 - \delta$$.

I'm not sure how covering numbers can be used here, any ideas are appreciated.

Looks like this can be used to prove the upper bound: https://en.wikipedia.org/wiki/Covering_number#Application_to_machine_learning