分配后服务下的动态匹配及其在难民安置中的应用
Dynamic Matching with Post-allocation Service and its Application to Refugee Resettlement
AI总结：
本文针对难民安置中的动态匹配问题，提出基于对偶变量学习的算法，在无需分布知识的情况下兼顾匹配奖励、动态资源拥堵和静态资源过度分配成本，并在真实数据上验证其优于现有方法。
摘要：
受我们与美国一家主要难民安置机构合作的启发，我们研究了一个动态匹配问题，其中每个新到达者（一个难民案例）必须立即且不可撤销地匹配到一个静态资源（一个具有固定年度配额的地点）。除了消耗静态资源外，每个案例还需要来自服务器（如翻译员）的分配后服务。鉴于服务时间的不确定性，服务器在给定时间可能不可用，因此我们将其称为动态资源。匹配后，案例将按照先到先服务的方式等待获得服务。对某个地点的突发性匹配可能导致其对应服务器出现不期望的拥堵。因此，中央规划者（该机构）面临一个动态匹配问题，其目标结合了匹配奖励（由配对特定的就业结果刻画）与动态资源的拥堵成本以及静态资源的过度分配成本。受观察到的跨年度难民群体构成波动的启发，我们旨在设计不依赖分布知识的算法。我们开发了基于学习的算法，这些算法在某些机制下是渐近最优的，易于解释，并且计算速度快。我们的设计基于学习底层优化问题的对偶变量；然而，主要挑战在于与动态资源相关的对偶变量具有时变性质。我们的理论发展结合了李雅普诺夫分析、对抗性在线学习和随机优化的技术。在应用方面，当在我们合作机构的真实数据上进行测试并纳入实际考虑因素时，我们的方法优于现有方法，使其成为在实验后替代当前实践的一个可行候选方案。
英文摘要：
Motivated by our collaboration with a major refugee resettlement agency in the U.S., we study a dynamic matching problem where each new arrival (a refugee case) must be matched immediately and irrevocably to one of the static resources (a location with a fixed annual quota). In addition to consuming the static resource, each case requires post-allocation services from a server, such as a translator. Given the uncertainty in service time, a server may not be available at a given time, thus we refer to it as a dynamic resource. Upon matching, the case will wait to avail service in a first-come-first-serve manner. Bursty matching to a location may result in undesirable congestion at its corresponding server. Consequently, the central planner (the agency) faces a dynamic matching problem with an objective that combines the matching reward (captured by pair-specific employment outcomes) with the cost for congestion for dynamic resources and over-allocation for the static ones. Motivated by the observed fluctuations in the composition of refugee pools across the years, we aim to design algorithms that do not rely on distributional knowledge. We develop learning-based algorithms that are asymptotically optimal in certain regimes, easy to interpret, and computationally fast. Our design is based on learning the dual variables of the underlying optimization problem; however, the main challenge lies in the time-varying nature of the dual variables associated with dynamic resources. Our theoretical development brings together techniques from Lyapunov analysis, adversarial online learning, and stochastic optimization. On the application side, when tested on real data from our partner agency and incorporating practical considerations, our method outperforms existing ones making it a viable candidate for replacing the current practice upon experimentation.
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