variables stop increasing and converge.

When a problem has zero duality gap, the dual problem can be rewritten as $$\begin{aligned}
\label{eq:opt_problem_dual_2}
D_\theta^* &= \min_\theta L(\theta, \lambda^*)\end{aligned}$$ if the dual maximizer $\lambda^*$ is known. This is simply a minimization of the objective function with a weighted constraint term. Thus, solving the constrained optimization problem is the same as solving an unconstrained problem with soft constraints that are weighted by the optimal dual variables.

Control with Sufficiently Accurate Models {#sec:control}
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The previous section describes a method for learning a sufficiently accurate model for controller design. In this section we describe how the learned model can be used to that end. A policy is a function from the state to the action space $\pi:\mathcal{S}\to \mathcal{A}$. A specific way to describe a desired policy is to minimize some cost, $c( {s},  {a}, \phi_\theta)$ associated with the performance of the system. This could be for instance the difference between the predicted state of the model and some desired state. The action selected has to typically satisfy some constraints imposed by the model, e.g., the action is bounded by the maximum torque of the motor in a robotic system, or obstacles in an environment. Denote 