Generally the idea is to specialize the algorithm to be faster for a particular application domain. Direct speedup learning has not been very successful. A better approach may be to do supervised or unsupervised learning to acquire declarative control knowledge. The classification above is only indicative. Learning is maximization.
Maximization is search.
A set of examples is often called a dataset. The examples are coded in some representation language, e.g. each example is written as a conjunction of real-valued features. Almost always the concept description is in a different and more complex language. The concept description language implicitly defines the space of hypotheses. Often, the nature of this space, i.e. which concepts can be expressed and which cannot, is more important than the search algorithm.