SEARCH, Blackbox Optimization, And Sample Complexity

The SEARCH (Search Envisioned As Relation & Class Hierarchizing) framework developed elsewhere (Kargupta, 1995) ooered an alternate perspective toward blackbox optimization (BBO)|optimization in presence of little domain knowledge. The SEARCH framework investigated the conditions essential for transcending the limits of random enumerative search 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 the reliability is presented. The two primary lessons of this work are, a BBO (1) must search for appropriate relations and (2) can only solve the so called class of order-k delineable problems in polynomial sample complexity. These results are applicable to any blackbox search algorithms, including evolutionary optimization techniques.