Non-differentiable controllers and rule-based policies are widely used for controlling real systems such as robots and telecommunication networks. In this paper, we present a practical reinforcement learning method which improves upon such existing policies with a model-based approach for better sample efficiency. Our method significantly outperforms state-of-the-art model-based methods, in terms of sample efficiency, on several widely used robotic benchmark tasks. We also demonstrate the effectiveness of our approach on a control problem in the telecommunications domain, where model-based methods have not previously been explored. Experimental results indicate that a strong initial performance can be achieved and combined with improved sample efficiency. We further motivate the design of our algorithm with a theoretical lower bound on the performance.