在事前公平与福利之间进行最优插值
Optimally Interpolating between Ex-Ante Fairness and Welfare
AI总结：
研究资源分配中事前公平与福利的权衡问题，提出通用框架及两种高效算法实现多准则下的最优插值，并在真实数据上验证了理论分析。
摘要：
对于将一组资源在具有不同偏好的个体之间进行分配这一基本问题，分配方案的质量关系到所实现的公平程度和集体福利。遗憾的是，在许多资源分配场景中，在实现公平目标的同时最大化福利在计算上是困难的。在本研究中，我们考虑事前公平的概念；常见的例子包括随机化轮询算法和抽签机制。我们提出了一个通用框架，以系统地研究多准则设置下公平与福利目标之间的插值。我们开发了两种高效算法（ε-Mix 和 Simple-Mix），它们在公平和福利方面实现了不同的权衡保证。ε-Mix 实现了关于公平和福利的最优多准则近似，而 Simple-Mix 则实现了常数因子内的最优性，且在底层的福利最大化机制和事前公平机制之外没有额外的计算开销。我们的框架对这两个底层机制不做任何假设，仅要求公平机制在所有分配方案的集合上产生一个分布。事实上，如果这些机制本身就是近似算法，我们的框架将保留其近似因子，在保证对底层机制质量敏感的同时，对它们保持 oblivious（不可见）。我们还针对上述事前公平机制在真实数据集上进行了广泛的实验分析，证实了我们的理论分析。
英文摘要：
For the fundamental problem of allocating a set of resources among individuals with varied preferences, the quality of an allocation relates to the degree of fairness and the collective welfare achieved. Unfortunately, in many resource-allocation settings, it is computationally hard to maximize welfare while achieving fairness goals. In this work, we consider ex-ante notions of fairness; popular examples include the \emph{randomized round-robin algorithm} and \emph{sortition mechanism}. We propose a general framework to systematically study the \emph{interpolation} between fairness and welfare goals in a multi-criteria setting. We develop two efficient algorithms ($\varepsilon-Mix$ and $Simple-Mix$) that achieve different trade-off guarantees with respect to fairness and welfare. $\varepsilon-Mix$ achieves an optimal multi-criteria approximation with respect to fairness and welfare, while $Simple-Mix$ achieves optimality up to a constant factor with zero computational overhead beyond the underlying \emph{welfare-maximizing mechanism} and the \emph{ex-ante fair mechanism}. Our framework makes no assumptions on either of the two underlying mechanisms, other than that the fair mechanism produces a distribution over the set of all allocations. Indeed, if these mechanisms are themselves approximation algorithms, our framework will retain the approximation factor, guaranteeing sensitivity to the quality of the underlying mechanisms, while being \emph{oblivious} to them. We also give an extensive experimental analysis for the aforementioned ex-ante fair mechanisms on real data sets, confirming our theoretical analysis.
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