We study the problem of learning, from observational data, fair and interpretable policies that effectively match heterogeneous individuals to scarce resources of different types. We model this problem as a multi-class multi-server queuing system where both individuals and resources arrive stochastically over time. Each individual, upon arrival, is assigned to a queue where they wait to be matched to a resource. The resources are assigned in a first come first served (FCFS) fashion according to an eligibility structure that encodes the resource types that serve each queue. We propose a methodology based on techniques in modern causal inference to construct the individual queues as well as learn the matching outcomes and provide a mixed-integer optimization (MIO) formulation to optimize the eligibility structure. The MIO problem maximizes policy outcome subject to wait time and fairness constraints. It is very flexible, allowing for additional linear domain constraints. We conduct extensive analyses using synthetic and real-world data. In particular, we evaluate our framework using data from the U.S. Homeless Management Information System (HMIS). We obtain wait times as low as an FCFS policy while improving the rate of exit from homelessness for underserved or vulnerable groups (7% higher for the Black individuals and 15% higher for those below 17 years old) and overall.
翻译:我们研究从观察数据中学习的公平和可解释的政策问题,这种政策有效地将不同的个人与不同种类的稀缺资源相匹配;我们将这一问题作为多级多服务器排队系统,使个人和资源随时间推移而来;每个人一到就被分配到等待资源匹配的队列中;资源首先按照一种标准结构,将服务于每个排队的资源类型编码起来,以最先到的资格结构(FFCFS)分配。我们根据现代因果推断技术提出一种方法,以构建单个排队和学习配对结果,并提供混合英特机优化(MIO)的配置,以优化资格结构;MIO问题在等待时间和公平限制的情况下,最大限度地实现政策结果的排队列;非常灵活,允许更多的线性限制;我们使用合成和实际世界数据进行广泛的分析;特别是,我们利用美国无房管理信息系统(HMIS)的数据来评估我们的框架;我们作为FCFSS政策的一个低点等待时间,用于构建单个排队列和学习配对结果,并提供混合英机优化的配制(MIO),以便优化资格结构结构结构结构结构优化;同时提高15年以下的黑人或老年群体摆脱无家可归或老年群体(7%)。