论文标题
一个统一的框架，用于分析和优化一类凸公平措施
A Unified Framework for Analyzing and Optimizing a Class of Convex Fairness Measures
论文作者
论文摘要
我们提出了一个新的框架，将不同的公平度量统一为适合优化环境的一般，参数化的凸公平措施。首先，我们提出了一类新的基于订单的公平度量，讨论它们的特性，并为此类措施提供公理表征。然后，我们介绍了凸公平度量的类别，讨论它们的特性，并将这些度量的等效双重表示作为基于双重订单的公平度量，而不是其双重组合。重要的是，这种双重表示通过其双重组进行了统一的数学表达和凸公平度量的替代几何表征。此外，它使我们能够开发一个统一的框架，以使用凸公平度量的目标或约束，包括统一的重新制定和解决方案方法，以优化问题。此外，我们还提供稳定性结果，以量化采用不同凸公平度量对最佳价值和解决方案的影响公平促进优化问题的影响。最后，我们提出了数值结果，证明了我们统一框架对传统框架的计算效率，并说明了我们的稳定性结果。
We propose a new framework that unifies different fairness measures into a general, parameterized class of convex fairness measures suitable for optimization contexts. First, we propose a new class of order-based fairness measures, discuss their properties, and derive an axiomatic characterization for such measures. Then, we introduce the class of convex fairness measures, discuss their properties, and derive an equivalent dual representation of these measures as a robustified order-based fairness measure over their dual sets. Importantly, this dual representation renders a unified mathematical expression and an alternative geometric characterization for convex fairness measures through their dual sets. Moreover, it allows us to develop a unified framework for optimization problems with a convex fairness measure objective or constraint, including unified reformulations and solution methods. In addition, we provide stability results that quantify the impact of employing different convex fairness measures on the optimal value and solution of the resulting fairness-promoting optimization problem. Finally, we present numerical results demonstrating the computational efficiency of our unified framework over traditional ones and illustrating our stability results.
