8. [M21] Consider online Algorithm G. Prove that, when considering the weight updating of any loop over the training set, the following properties hold true:

(i) ∀κ, if |L| < ∞and η → 0 then lim

η→0

ˆ wκ+1 − ˆwκ

η

= ∇E( ˆwκ ). (3.4.88)

(ii) For “large” training sets Eq. (3.4.88) is approximatively satisfied for “small” η.