In this paper we apply a multi-level structure to robotic manipulation learning. It consists of a hybrid dynamical system we denote skill and a parameter learning layer that leverages the underlying structure to simplify the problem at hand. For the learning layer we introduce a novel algorithm based on the idea of learning to partition the parameter solution space to quickly and efficiently find good and robust solutions to complex manipulation problems. In a benchmark comparison we show a significant performance increase compared with other black-box optimization algorithms such as HiREPS and particle swarm optimization. Furthermore, we validate and compare our approach on a very hard real-world manipulation problem, namely inserting a key into a lock, against state-of-the-art deep reinforcement learning.