We present an automatic method for interactive control of physical humanoid robots based on high-level tasks that does not require manual specification of motion trajectories or specially-designed control policies. The method is based on the combination of a model-based policy that is trained off-line in simulation and sends high-level commands to a model-free controller that executes these commands on the physical robot. This low-level controller simultaneously learns and adapts a local model of dynamics on-line and computes optimal controls under the learned model. The high-level policy is trained using a combination of trajectory optimization and neural network learning, while considering physical limitations such as limited sensors and communication delays. The entire system runs in real-time on the robot's computer and uses only on-board sensors. We demonstrate successful policy execution on a range of tasks such as leaning, hand reaching, and robust balancing behaviors atop a tilting base on the physical robot and in simulation.