Polynomial complexity blackbox search: lessons from the SEARCH framework

The SEARCH (Search Envisioned As Relation and Class Hierarchizing) framework, developed by H. Kargupta (1995) offered an alternate perspective toward blackbox optimization-i.e. optimization in the presence of little domain knowledge. The SEARCH framework investigates the conditions that are essential for transcending the limits of random enumerative searching using a framework developed in terms of relations, classes and partial ordering. This paper presents a summary of some of the main results of that work. A closed-form bound on the sample complexity in terms of the cardinality of the relation space, class space, desired quality of the solution and reliability is presented. This also leads to the identification of the class of order-k delineable problems that can be solved in polynomial sample complexity. These results are applicable to any blackbox search algorithms, including evolutionary optimization techniques.