In decision-making under uncertainty, several criteria have been studied to aggregate the performance of a solution over multiple possible scenarios. This paper introduces a novel variant of ordered weighted averaging (OWA) for optimization problems. It generalizes the classic OWA approach, which includes the robust min–max optimization as a special case, as well as the min–max regret optimization. We derive new complexity results for this setting, including insights into the inapproximability and approximability of this problem. In particular, we provide stronger positive approximation results that asymptotically improve the previously best-known bounds for the classic OWA approach.

中文翻译：

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使用有序加权平均的稳健最小-最大（遗憾）优化


在不确定性下的决策中，已经研究了几个标准来汇总解决方案在多种可能情况下的性能。本文介绍了一种用于优化问题的有序加权平均 （OWA） 的新变体。它概括了经典的 OWA 方法，其中包括作为特殊情况的稳健 min-max 优化，以及 min-max 遗憾优化。我们为此设置得出了新的复杂度结果，包括对此问题的不近似性和近似性的见解。特别是，我们提供了更强的正近似结果，渐近地改善了经典 OWA 方法以前最广为人知的边界。