this paper we formulate 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. The constraints that are imposed in the model accuracy are intended to ensure that the model is sufficiently accurate for a variety of control tasks. To that end, we consider a partition $\cup_{i=0}^P\mathcal{K}_i=\mathcal{S}\times\mathcal{A}$ of the state-action space and constraints $h:\mathcal{S}\times\mathcal{A}\times\mathbb{R}^N\to \mathbb{R}^P$, where each component of the constraint is imposed on a different region of the space-action space. With these definitions, we propose the following optimization problem $$\begin{aligned}
\label{eq:constrained_model_learning}
    P^*_\theta &=\min_\theta  \mathbb{E}_{( s,  a) \sim D} l(s,a,\phi_\theta) \mathbb{I}_{\mathcal{K}_0}(s,a) \\
    & \text{s.t. } \mathbb{E}_{(s,a) \sim D} h_i(s,a,\theta) \mathbb{I}_{\mathcal{K}_i}(s,a) \leq \epsilon \quad \forall i\ldots P, \nonumber\end{aligned}$$ where $\mathbb{I}_{\mathcal{K}_i}(s,a)$ with $i=0\ldots P$ are indicator functions taking the value $1$ if $(s,a)\in\mathcal{K}_i$ and $0$ otherwise. In the next section we present a primal dual algorithm to solve the optimization problem . Before doing so, we consider an example to illustrate the sufficiently accurate learning framework.

**Example 1.** As an example of the previous formulation we consider the minimization of a normalized error. The error tolerance in a forward model is directly related to the magnitude 