Summary We consider an experimental setting in which a matching of resources to participants has to be chosen repeatedly and returns from the individual chosen matches are unknown, but can be learned. Our setting covers two-sided and one-sided matching with (potentially complex) capacity constraints, such as refugee resettlement, social housing allocation, and foster care. We propose a variant of the Thompson sampling algorithm to solve such adaptive combinatorial allocation problems. We give a tight, prior-independent, finite-sample bound on the expected regret for this algorithm. Although the number of allocations grows exponentially in the number of matches, our bound does not. In simulations based on refugee resettlement data using a Bayesian hierarchical model, we find that the algorithm achieves half of the employment gains (relative to the status quo) that could be obtained in an optimal matching based on perfect knowledge of employment probabilities.

中文翻译：

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与半土匪匹配

总结 我们考虑一个实验环境，其中必须重复选择资源与参与者的匹配，并且从个人选择的匹配中返回的结果是未知的，但可以学习。我们的设置涵盖了与（可能复杂的）能力限制的双边和单边匹配，例如难民安置、社会住房分配和寄养。我们提出了一种 Thompson 采样算法的变体来解决这种自适应组合分配问题。我们对该算法的预期遗憾给出了一个严格的、先验独立的、有限样本界限。尽管分配的数量随着匹配的数量呈指数增长，但我们的界限并没有。在使用贝叶斯层次模型基于难民安置数据的模拟中，