Learning Resource Allocation Policies from Observational Data with an Application to Homeless Services Delivery

TL;DR

This paper develops a causal inference-based framework to learn fair, interpretable resource allocation policies from observational data, demonstrated through homeless services data to improve outcomes for vulnerable groups.

Contribution

It introduces a novel methodology combining causal inference and mixed-integer optimization to design fair resource allocation policies from observational data.

Findings

Achieved wait times comparable to FCFS policies.

Improved exit rates from homelessness for underserved groups.

Demonstrated effectiveness on real-world HMIS data.

Abstract

We study the problem of learning, from observational data, fair and interpretable policies that effectively match heterogeneous individuals to scarce resources of different types. We model this problem as a multi-class multi-server queuing system where both individuals and resources arrive stochastically over time. Each individual, upon arrival, is assigned to a queue where they wait to be matched to a resource. The resources are assigned in a first come first served (FCFS) fashion according to an eligibility structure that encodes the resource types that serve each queue. We propose a methodology based on techniques in modern causal inference to construct the individual queues as well as learn the matching outcomes and provide a mixed-integer optimization (MIO) formulation to optimize the eligibility structure. The MIO problem maximizes policy outcome subject to wait time and fairness constraints. It is very flexible, allowing for additional linear domain constraints. We conduct extensive analyses using synthetic and real-world data. In particular, we evaluate our framework using data from the U.S. Homeless Management Information System (HMIS). We obtain wait times as low as an FCFS policy while improving the rate of exit from homelessness for underserved or vulnerable groups (7% higher for the Black individuals and 15% higher for those below 17 years old) and overall.