Consider a system which takes data as an input, processes the data with a model, and outputs a decision for a particular objective. We call the measure of the amount of data used to complete the objective with some performance metric as data efficiency.  Across many domains, it is advantageous to reduce the amount of data to achieve the same or better level of performance. In this thesis, we exploit the model of the system in order to improve the data efficiency across three distinct domains of interest: robot navigation in ellipsoidal worlds, reinforcement learning, and Lie group convolutions.