Motivated by the problem of assigning mediators to cases in the Kenyan judicial, we study an online resource allocation problem where incoming tasks (cases) must be immediately assigned to available, capacity-constrained resources (mediators). The resources differ in their quality, which may need to be learned. In addition, resources can only be assigned to a subset of tasks that overlaps to varying degrees with the subset of tasks other resources can be assigned to. The objective is to maximize task completion while satisfying soft capacity constraints across all the resources. The scale of the real-world problem poses substantial challenges, since there are over 2000 mediators and a multitude of combinations of geographic locations (87) and case types (12) that each mediator is qualified to work on. Together, these features, unknown quality of new resources, soft capacity constraints, and a high-dimensional state space, make existing scheduling and resource allocation algorithms either inapplicable or inefficient. We formalize the problem in a tractable manner using a quadratic program formulation for assignment and a multi-agent bandit-style framework for learning. We demonstrate the key properties and advantages of our new algorithm, SMaRT (Selecting Mediators that are Right for the Task), compared with baselines on stylized instances of the mediator allocation problem. We then consider its application to real-world data on cases and mediators from the Kenyan judiciary. SMaRT outperforms baselines and allows control over the tradeoff between the strictness of capacity constraints and overall case resolution rates, both in settings where mediator quality is known beforehand and in bandit-like settings where learning is part of the problem definition. On the strength of these results, we plan to run a randomized controlled trial with SMaRT in the judiciary in the near future.

翻译：受肯尼亚司法系统中调解员案件分配问题的启发，我们研究了一个在线资源分配问题：到达的任务（案件）必须立即分配给可用且容量受限的资源（调解员）。资源的质量存在差异，且可能需要通过学习来获知。此外，资源只能分配给任务的一个子集，该子集与其他资源可分配的任务子集存在不同程度的重叠。目标是在满足所有资源的软容量约束的同时，最大化任务完成量。实际问题的规模带来了巨大挑战，因为存在超过2000名调解员，且每名调解员有资格处理的地理位置（87个）与案件类型（12种）存在多种组合。这些特征——新资源的未知质量、软容量约束以及高维状态空间——共同使得现有的调度与资源分配算法要么不适用，要么效率低下。我们通过二次规划形式的分配公式与多智能体赌博机风格的学习框架，以可处理的方式形式化了该问题。我们在调解员分配问题的典型实例上，展示了新算法SMaRT（为任务选择合适的调解员）相较于基线方法的关键特性与优势。随后，我们将其应用于肯尼亚司法系统的真实案件与调解员数据。无论是在调解员质量事先已知的场景，还是在学习作为问题定义一部分的类赌博机场景中，SMaRT均优于基线方法，并允许在容量约束的严格性与整体案件解决率之间进行权衡控制。基于这些结果，我们计划在不久的将来于司法系统中使用SMaRT开展一项随机对照试验。