论文标题

设定公平的激励措施以最大化改进

Setting Fair Incentives to Maximize Improvement

论文作者

Ahmadi, Saba, Beyhaghi, Hedyeh, Blum, Avrim, Naggita, Keziah

论文摘要

我们考虑通过设定短期目标来帮助代理商改善的问题。给定一组目标技能水平,我们假设每个代理商都会尝试从其初始技能水平提高到触及范围内最接近的目标水平,或者如果没有目标水平,则无能为力。我们考虑了两个模型:共同的改进能力模型,在该模型中,代理对它们的改进程度和个性化改进能力模型具有相同的限制,而代理具有个性化的限制。我们的目标是优化社会福利和公平目标的目标级别,在这种目标中,社会福利被定义为总数的总数,并且在代理人属于不同基础人群的地方被视为公平目标。该问题的主要技术挑战是目标水平集中社会福利的非单调性,即增加新的目标水平可能会减少总数的进步,因为某些代理商可能会更容易改善。在考虑多个组时,这尤其具有挑战性,因为为每个组隔离目标水平并输出联盟可能会导致一个组的任意改善,从而失败了公平目标。考虑到这些属性,我们为社会福利和公平目标提供了最佳和近乎最佳改进的算法。这些算法结果对共同和个性化的改进能力模型都起作用。此外,我们展示了目标水平的位置,对于每个群体的社会福利大致最佳。与算法结果不同,该结构语句仅在共同的改进能力模型中,并且我们在个性化的改进能力模型中显示了反例。最后,我们将算法扩展到学习设置,在这些设置中,我们只能访问对代理的初始技能水平。

We consider the problem of helping agents improve by setting short-term goals. Given a set of target skill levels, we assume each agent will try to improve from their initial skill level to the closest target level within reach or do nothing if no target level is within reach. We consider two models: the common improvement capacity model, where agents have the same limit on how much they can improve, and the individualized improvement capacity model, where agents have individualized limits. Our goal is to optimize the target levels for social welfare and fairness objectives, where social welfare is defined as the total amount of improvement, and fairness objectives are considered where the agents belong to different underlying populations. A key technical challenge of this problem is the non-monotonicity of social welfare in the set of target levels, i.e., adding a new target level may decrease the total amount of improvement as it may get easier for some agents to improve. This is especially challenging when considering multiple groups because optimizing target levels in isolation for each group and outputting the union may result in arbitrarily low improvement for a group, failing the fairness objective. Considering these properties, we provide algorithms for optimal and near-optimal improvement for both social welfare and fairness objectives. These algorithmic results work for both the common and individualized improvement capacity models. Furthermore, we show a placement of target levels exists that is approximately optimal for the social welfare of each group. Unlike the algorithmic results, this structural statement only holds in the common improvement capacity model, and we show counterexamples in the individualized improvement capacity model. Finally, we extend our algorithms to learning settings where we have only sample access to the initial skill levels of agents.

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