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This paper proposes a neural network based reinforcement learning controller that is able to learn control policies in a highly data efficient manner. This allows to apply reinforcement learning directly to real plants -neither a transition model nor a simulation model of the plant is needed for training. The only training information provided to the controller are transition experiences collected from interactions with the real plant. By storing these transition experiences explicitly, they can be reconsidered for updating the neural Q-function in every training step. This results in a stable learning process of a neural Q-value function. The algorithm is applied to learn the highly nonlinear and noisy task of swinging-up and balancing a real inverted pendulum. The amount of real time interaction needed to learn a highly effective policy from scratch was less than 14 minutes.