Learning complex control policies from non-linear and redundant sensory input is an important challenge for reinforcement learning algorithms. Non-parametric methods that approximate values functions or transition models can address this problem, by adapting to the complexity of the data set. Yet, many current non-parametric approaches rely on unstable greedy maximization of approximate value functions, which might lead to poor convergence or oscillations in the policy update. A more robust policy update can be obtained by limiting the information loss between successive state-action distributions. In this paper, we develop a policy search algorithm with policy updates that are both robust and non-parametric. Our method can learn non- parametric control policies for infinite horizon continuous Markov decision processes with non-linear and redundant sensory representations. We investigate how we can use approximations of the kernel function to reduce the time requirements of the demanding non-parametric computations. In our experiments, we show the strong performance of the proposed method, and how it can be approximated efficiently. Finally, we show that our algorithm can learn a real-robot under-powered swing-up task directly from image data.