Control-based approaches to grasp synthesis create grasping behavior by sequencing and combining control primitives. In the absence of any other structure, these approaches must evaluate a large number of feasible control sequences as a function of object shape, object pose, and task. This paper explores a new approach to grasp synthesis that limits consideration to variations on a generalized localize-reach-grasp control policy. A new learning algorithm, known as schema structured learning, is used to learn which instantiations of the generalized policy are most likely to lead to a successful grasp in different problem contexts. Experiments are described where Dexter, a dexterous bimanual humanoid, learns to select appropriate grasp strategies for different objects as a function of object eccentricity and orientation. In addition, it is shown that grasp skills learned in this way generalize well to new objects. Results are presented showing that after learning how to grasp a small, representative set of objects, the robot’s performance quantitatively improves for similar objects that it has not experienced before.