lines represent predicted trajectories. The paddle actions, $a$, are optimized with gradient descent on a defined loss function. For the task of bouncing the ball consistently, a sufficiently accurate model that guarantees prediction error within some bound $\epsilon$ may be sufficient. []{data-label="fig:main"}](images/icmldrawings.png){width="35.00000%"}

In cases where the task parameters, such as goal location or actuation limits, change, a new controller involves simply solving a different optimization problem instead of relearning an inverse model. While there has been some work to learn task robust policies for inverse models, such as using Goal-Conditioned Policies [@nair2018visual; @pathak2018zero], it is not clear how one can enforce general constraints for the inverse model.

Learning a model is fundamentally different from learning a controller in that the controller is an end in itself but a model is useful only as an intermediate step to learn a controller. Therefore, learning a model with arbitrary accuracy is not necessarily warranted. Rather, we want to learn a model that is sufficiently accurate for controller design. This paper formulates the problem of learning a model as a constrained optimization problem in which the required accuracy of the model is imposed as a set of constraints (Section \[sec:model\_learning\]). The constraints that are 