1. (*) Show that if H is PAC learnable (in the standard one-oracle model), then H is PAC learnable in the two-oracle model.
2. (**) Define h+ to be the always-plus hypothesis and h− to be the always-minus hypothesis. Assume that h+ ,h− ∈ H. Show that if H is PAC learnable in the two-oracle model, then H is PAC learnable in the standard one-oracle model.
3.1 In this exercise, we show that the (_, δ) requirement on the convergence of errors in our definitions of PAC learning, is, in fact, quite close to a simpler looking requirement about averages (or expectations). Prove that the following two statements are equivalent (for any learning algorithm A, any probability distribution D, and any loss function whose range is [0, 1]):
