Matching with semi-bandits

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