Abstract: We address a class of manipulation problems where the robot perceives the scene with a depth sensor and can move its end effector in a space with six degrees of freedom – 3D position and orientation. Our approach is to formulate the problem as a Markov decision process (MDP) with abstract yet generally applicable state and action representations. Finding a good solution to the MDP requires adding constraints on the allowed actions. We develop a specific set of constraints called hierarchical SE(3) sampling (HSE3S) which causes the robot to learn a sequence of gazes to focus attention on the task-relevant parts of the scene. We demonstrate the effectiveness of our approach on three challenging pick-place tasks (with novel objects in clutter and nontrivial places) both in simulation and on a real robot, even though all training is done in simulation.