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

arXiv: https://arxiv.org/abs/2201.10053 · HTML: https://mlsanity.com/paper/2201.10053/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 47 references that are in the map.
- First posted on arXiv 25 Jan 2022.

## Builds on (most cited first, 6 of 6)

- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Exploring Algorithmic Fairness in Robust Graph Covering Problems](https://mlsanity.com/paper/2006.06865/) (2020)
- [Fair Influence Maximization: A Welfare Optimization Approach](https://mlsanity.com/paper/2006.07906/) (2020)
- [Learning Optimal Prescriptive Trees from Observational Data](https://mlsanity.com/paper/2108.13628/) (2021)
- [Fairness-aware Summarization for Justified Decision-Making](https://mlsanity.com/paper/2107.06243/) (2021)

## Built on by (most cited first, 5 of 5)

- [Fairness and Sequential Decision Making: Limits, Lessons, and Opportunities](https://mlsanity.com/paper/2301.05753/) (2023)
- [Off-Policy Evaluation with Policy-Dependent Optimization Response](https://mlsanity.com/paper/2202.12958/) (2022)
- [Fairness in Contextual Resource Allocation Systems: Metrics and Incompatibility Results](https://mlsanity.com/paper/2212.01725/) (2022)
- [Fair and Welfare-Efficient Constrained Multi-matchings under Uncertainty](https://mlsanity.com/paper/2411.02654/) (2024)
- [Toward AI Matching Policies in Homeless Services: A Qualitative Study with Policymakers](https://mlsanity.com/paper/2508.07129/) (2025)

## Abstract (arXiv)

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.