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.

Fairness in Contextual Resource Allocation Systems: Metrics and Incompatibility Results

We study critical systems that allocate scarce resources to satisfy basic needs, such as homeless services that provide housing. These systems often support communities disproportionately affected by systemic racial, gender, or other injustices, so it is crucial to design these systems with fairness considerations in mind. To address this problem, we propose a framework for evaluating fairness in contextual resource allocation systems that is inspired by fairness metrics in machine learning. This framework can be applied to evaluate the fairness properties of a historical policy, as well as to impose constraints in the design of new (counterfactual) allocation policies. Our work culminates with a set of incompatibility results that investigate the interplay between the different fairness metrics we propose. Notably, we demonstrate that: 1) fairness in allocation and fairness in outcomes are usually incompatible; 2) policies that prioritize based on a vulnerability score will usually result in unequal outcomes across groups, even if the score is perfectly calibrated; 3) policies using contextual information beyond what is needed to characterize baseline risk and treatment effects can be fairer in their outcomes than those using just baseline risk and treatment effects; and 4) policies using group status in addition to baseline risk and treatment effects are as fair as possible given all available information. Our framework can help guide the discussion among stakeholders in deciding which fairness metrics to impose when allocating scarce resources.