Bounding the cost of learned rules

In this article we approach one key aspect of the utility problem in explanationbased learning (EBL) | the expensive-rule problem | as an avoidable defect in the learning procedure. In particular, we examine the relationship between the cost of solving a problem without learning versus the cost of using a learned rule to provide the same solution, and refer to a learned rule as expensive if its use is more costly than the original problem solving from which it was learned. The key idea we explore is that expensiveness is inadvertently and unnecessarily introduced into learned rules by the learning algorithms themselves. This becomes a particularly powerful idea when combined with an analysis tool which identi es these hidden sources of expensiveness, and modi cations of the learning algorithms which eliminate them. The result is learning algorithms for which the cost of learned rules is bounded by the cost of the problem solving that they replace. We investigate this idea through an analysis of EBLSoar, an implementation of explanation-based learning within the Soar architecture. A transformational analysis is used to identify where EBLSoar inadvertently introduces substantial additional costs in the process of converting a problem solving episode into a learned rule | excessive costs which all ultimately turn out to stem from losses of information during learning. Based on these results, a modi ed EBLSoar algorithm| Bounded EBLSoar (BEBLSoar) | is developed from which all sources of expensiveness have been eliminated. The cost of using a rule learned by BEBLSoar is provably bounded by the cost of the problem solving it replaces.