Induction as optimization

A representative (but unimodal) problem, the fifteen puzzle, is used to test six different learning systems: some that fit, count, or partition data in instance space; some that optimize measures derived from data in hypothesis space; and some that perform combinations of such procedures. The six systems are described, tested, and analyzed. Through several experiments, specific properties are extracted. By combining two or three kinds of techniques, the extent to which they complement each other is gauged. It is concluded that combinations of strengths can overcome difficulties in domains that are simultaneously probabilistic, dynamic, noisy, and biased