Trajectory planning and optimization is a fundamental problem in articulated robotics. Algorithms used typically for this problem compute optimal trajectories from scratch in a new situation. In effect, extensive data is accumulated containing situations together with the respective optimized trajectories - but this data is in practice hardly exploited. The aim of this paper is to learn from this data. Given a new situation we want to predict a suitable trajectory which only needs minor refinement by a conventional optimizer. Our approach has two essential ingredients. First, to generalize from previous situations to new ones we need an appropriate situation descriptor - we propose a sparse feature selection approach to find such well-generalizing features of situations. Second, the transfer of previously optimized trajectories to a new situation should not be made in joint angle space - we propose a more efficient task space transfer of old trajectories to new situations. Experiments on trajectory optimization for a simulated humanoid reaching problem show that we can predict reasonable motion prototypes in new situations for which the refinement is much faster than an optimization from scratch.