imposed in the model accuracy are intended to ensure that the model is [*sufficiently accurate*]{} for a variety of control tasks. The main advantage of learning sufficiently accurate models is an appropriate tailoring of the sample complexity. A bonus advantage derived from our problem formulation is that the accuracy constraints that are imposed in model learning allow for trading off the accuracy of the model in different parts of the state space. For example, in Fig. \[fig:main\] we consider the problem of determining the dynamical trajectories followed by a ball that is hit by a paddle in order to design a controller that would allow us to keep the ball in the air by repeatedly hitting it when the vertical position crosses a certain threshold. We argue that for this problem it is advantageous to learn models that predict with an accuracy dependent on the velocity of the ball.

Contributions
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This paper proposes a constraint-based formulation for learning and controlling dynamical systems. Contact dynamics is difficult to model and we show in this paper how optimizing a controller with constraints is a more viable solution to even an analytic controller on the learned model. The contributions of this paper 