This chapter reviews a system named ULS that addresses the utility of learning by approximating the results of explanation-based learning. One of the major applications of explanation-based learning techniques has been to improve the performance of problem solvers through the acquisition of search control knowledge. The problem solver's performance may actually degrade if the cost of testing the applicability of the learned search control knowledge is greater than the savings realized by reducing the search. One way to address this problem is to search through the space of sets of search control rules itself, explicitly guided by utility criteria. ULS can form a viable system to such an end. It consists of a problem solver, an explanation-based learner, and a rule transformer. The ULS problem solver is a STRIPS-like problem solver whose search can be guided by applying rules that prefer or reject a search control decision. The rule transformation component of ULS applies generalization and specialization transformations to change the rules into ones that are more efficient to test, while still reducing the problem solver's need to search. The transformed rules are approximations to the original rules because the decision to apply the transformations is based on statistical evidence. ULS estimates the utility of transformed rules: testing the applicability of a fewer number of conditions is usually less expensive, provided the dropped condition rarely affects the truth value of the rule's conditions.