逆多目标optimization：从数据中推断决策准则
Inverse multiobjective optimization: Inferring decision criteria from data
摘要：
这是一个非常具有挑战性的任务，以确定某个决定的基础上的目标，特别是如果几个，可能相互冲突的标准是同样重要的，一个连续的最佳折衷的决定存在。这个任务可以理解为多目标优化的逆问题，目标是找到给定Pareto集的目标向量。为此，我们提出了一种方法来构造多目标最优化问题（MOP）的目标向量，使得Pareto临界集包含一组给定的数据点或决策向量。其核心思想是将多目标KKT条件中的目标向量视为变量，然后搜索使所得方程组的欧几里德范数最小的目标。通过在有限维的基础上表达的目标，我们把这个问题转化为一个齐次，线性方程组，可以有效地解决。这种方法有许多重要的潜在应用。除了目标的识别（从干净的和有噪声的数据），该方法可用于昂贵的MOPs，这产生显着的加速代理模型的建设。这两个应用程序都说明了使用几个例子。
英文摘要：
It is a very challenging task to identify the objectives on which a certain decision was based, in particular if several, potentially conflicting criteria are equally important and a continuous set of optimal compromise decisions exists. This task can be understood as the inverse problem of multiobjective optimization, where the goal is to find the objective vector of a given Pareto set. To this end, we present a method to construct the objective vector of a multiobjective optimization problem (MOP) such that the Pareto critical set contains a given set of data points or decision vectors. The key idea is to consider the objective vector in the multiobjective KKT conditions as variable and then search for the objectives that minimize the Euclidean norm of the resulting system of equations. By expressing the objectives in a finite-dimensional basis, we transform this problem into a homogeneous, linear system of equations that can be solved efficiently. There are many important potential applications of this approach. Besides the identification of objectives (both from clean and noisy data), the method can be used for the construction of surrogate models for expensive MOPs, which yields significant speed-ups. Both applications are illustrated using several examples.
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