A Study of Empirical Learning for an Involved Problem

In rea l -wor ld domains a concept to be learned may be unwieldy and the environment may be less than ideal. One combinat ion of difficulties occurs if the concept is probabi l ist ic and the learning si tuat ion is dynamic. In this case, the data may be noisy and biased. These difficulties arise when learning evaluation functions, which can be considered as concepts. A representative problem, the fifteen puzzle, is used to test six different learning systems: some that fit, count, or par t i t ion data in instance, space; some that optimize measures derived f rom data in hypothesis space; and some that perform combinations of such procedures. These six systems are described, tested, and analyzed. F r o m quant i tat ive differences in several experiments, we extract specific properties. By combining two or three kinds of techniques, we gauge the extent to which they complement each other. Combinations of strengths can overcome difficulties in domains that are simultaneously probabi l ist ic, dynamic, noisy, and biased.