Designing Fair, Efficient, and Interpretable Policies for Prioritizing Homeless Youth for Housing Resources

We consider the problem of designing fair, efficient, and interpretable policies for prioritizing heterogeneous homeless youth on a waiting list for scarce housing resources of different types. We focus on point-based policies that use features of the housing resources (e.g., permanent supportive housing, rapid rehousing) and the youth (e.g., age, history of substance use) to maximize the probability that the youth will have a safe and stable exit from the housing program. The policies can be used to prioritize waitlisted youth each time a housing resource is procured. Our framework provides the policy-maker the flexibility to select both their desired structure for the policy and their desired fairness requirements. Our approach can thus explicitly trade-off interpretability and efficiency while ensuring that fairness constraints are met. We propose a flexible data-driven mixed-integer optimization formulation for designing the policy, along with an approximate formulation which can be solved efficiently for broad classes of interpretable policies using Bender’s decomposition. We evaluate our framework using real-world data from the United States homeless youth housing system. We show that our framework results in policies that are more fair than the current policy in place and than classical interpretable machine learning approaches while achieving a similar (or higher) level of overall efficiency.