Lazy and Eager Learning

Instance-based methods are also known as lazy learning because they do not generalize until needed.
All the other learning methods we have seen (and even radial basis function networks) are eager learning methods because they generalize before seeing the query.
The eager learner must create a global approximation.
The lazy learner can create many local approximations.
If they both use the same $H$ then, in effect, the lazy can represent more complex function.
For example, if $H$ consists of linear function then a lazy learner can construct what amounts to a non-linear global function.