Learning Optimal and Fair Policies for Online Allocation of Scarce Societal Resources from Data Collected in Deployment

We study the problem of allocating scarce societal resources of different
types (e.g., permanent housing, deceased donor kidneys for transplantation,
ventilators) to heterogeneous allocatees on a waitlist (e.g., people
experiencing homelessness, individuals suffering from end-stage renal disease,
Covid-19 patients) based on their observed covariates. We leverage
administrative data collected in deployment to design an online policy that
maximizes expected outcomes while satisfying budget constraints, in the long
run. Our proposed policy waitlists each individual for the resource maximizing
the difference between their estimated mean treatment outcome and the estimated
resource dual-price or, roughly, the opportunity cost of using the resource.
Resources are then allocated as they arrive, in a first-come first-serve
fashion. We demonstrate that our data-driven policy almost surely
asymptotically achieves the expected outcome of the optimal out-of-sample
policy under mild technical assumptions. We extend our framework to incorporate
various fairness constraints. We evaluate the performance of our approach on
the problem of designing policies for allocating scarce housing resources to
people experiencing homelessness in Los Angeles based on data from the homeless
management information system. In particular, we show that using our policies
improves rates of exit from homelessness by 1.9% and that policies that are
fair in either allocation or outcomes by race come at a very low price of
fairness.