Model-based reinforcement learning (RL) has proven to be a data efficient approach for learning control tasks but is difficult to utilize in domains with complex observations such as images. In this paper, we present a method for learning representations that are suitable for iterative model-based policy improvement, in that these representations are optimized for inferring simple dynamics and cost models given the data from the current policy. This enables a model-based RL method based on the linear-quadratic regulator (LQR) to be used for systems with image observations. We evaluate our approach on a suite of robotics tasks, including manipulation tasks on a real Sawyer robot arm directly from images, and we find that our method results in better final performance than other model-based RL methods while being significantly more efficient than model-free RL.