of the trajectory. To this end, we will add a weighting vector $\alpha$ that will penalize more the errors that are near the present time. But still, this is not sufficient because, depending on the present time, some parameters will not have any effect on the trajectory. As a matter of fact, from 0 to FL60, a predefined schedule is applied and only the mass parameter has an effect in BADA. The scope of the parameter $V_1$ is from FL60 to FL100, the scope of $V_2$ is from FL100 to the transition altitude (around FL277) and finally, the scope of $V_m$ is over the transition altitude. Furthermore, we add the constraint that $V_2$ is greater than $V_1$ to the optimization problem. To avoid that the optimization algorithm assigns them some arbitrary values resulting in unrealistic trajectories, we use a regulation method that penalizes any deviation from the default parameters. A meta-parameter $\lambda$ is associated to the weight of the penalty, which controls the tradeoff between exploration and exploitation. Consequently, the resulting objective function is:

$$\label{eq:learning}
\theta_{0,t}^* = \underset{\theta \in \Theta}{\operatorname{argmin}} \left[ \sum_{i=0}^t \alpha_i \left| \mathcal{H}(\theta;s_0)_i - O_i \right| + \lambda \sum_{i=0}^{|\theta|} \left| \theta_i - \theta_i^d \right| \right]$$

where $\theta^d$ is 