Classical methods of calibration usually imply the minimisation of an objective function with respect to some control parameters. This function measures the error between some observations and the results obtained by a numerical model. In the presence of uncontrollable additional parameters that we model as random inputs, the objective function becomes a random variable, and notions of robustness have to be introduced for such an optimisation problem.

In this paper, we are going to present how to take into account those uncertainties by defining the relative-regret. This quantity allow us to compare the value of the objective function to its best performance achievable given a realisation of the random additional parameters. By controlling this relative-regret using a probabilistic constraint, we can then define a new family of estimators, whose robustness with respect to the random inputs can be adjusted.

经典的校准方法通常意味着目标函数相对于某些控制参数的最小化。此功能可测量某些观测值与数值模型获得的结果之间的误差。在存在我们将其建模为随机输入的不可控制的附加参数的情况下，目标函数变为随机变量，因此必须针对此类优化问题引入鲁棒性的概念。

在本文中，我们将介绍如何通过定义相对遗憾来考虑这些不确定性。在实现随机附加参数的情况下，此数量使我们能够将目标函数的值与其可实现的最佳性能进行比较。通过使用概率约束来控制此相对后悔，我们可以定义一个新的估计量族，可以调整其相对于随机输入的鲁棒性。