Adaptive Combinatorial Allocation

TL;DR

This paper introduces a Thompson sampling-based method for adaptive combinatorial allocation problems with unknown returns and complex constraints, providing regret bounds independent of the exponential growth in allocations, demonstrated on refugee resettlement data.

Contribution

It presents a novel prior-independent finite-sample regret bound for a Thompson sampling approach in complex allocation settings with constraints.

Findings

Regret bounds do not depend on the exponential number of allocations.

Algorithm performs well on refugee resettlement data.

Applicable to various matching problems with complex constraints.

Abstract

We consider settings where an allocation has to be chosen repeatedly, returns are unknown but can be learned, and decisions are subject to constraints. Our model covers two-sided and one-sided matching, even with complex constraints. We propose an approach based on Thompson sampling. Our main result is a prior-independent finite-sample bound on the expected regret for this algorithm. Although the number of allocations grows exponentially in the number of participants, the bound does not depend on this number. We illustrate the performance of our algorithm using data on refugee resettlement in the United States.