# Fair Algorithms for Learning in Allocation Problems

arXiv: https://arxiv.org/abs/1808.10549 · HTML: https://mlsanity.com/paper/1808.10549/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2018.

## Built on by (most cited first, 29 of 29)

- [Off-Policy Confidence Interval Estimation with Confounded Markov Decision Process](https://mlsanity.com/paper/2202.10589/) (2022)
- [A Sociotechnical View of Algorithmic Fairness](https://mlsanity.com/paper/2110.09253/) (2021)
- [What-is and How-to for Fairness in Machine Learning: A Survey, Reflection, and Perspective](https://mlsanity.com/paper/2206.04101/) (2022)
- [Runtime Monitoring of Dynamic Fairness Properties](https://mlsanity.com/paper/2305.04699/) (2023)
- [Towards Return Parity in Markov Decision Processes](https://mlsanity.com/paper/2111.10476/) (2021)
- [A Classification of Feedback Loops and Their Relation to Biases in Automated Decision-Making Systems](https://mlsanity.com/paper/2305.06055/) (2023)
- [Recommendation Fairness: From Static to Dynamic](https://mlsanity.com/paper/2109.03150/) (2021)
- [Equity and Artificial Intelligence in Education: Will "AIEd" Amplify or Alleviate Inequities in Education?](https://mlsanity.com/paper/2104.12920/) (2021)
- [Cooperative Multi-Agent Fairness and Equivariant Policies](https://mlsanity.com/paper/2106.05727/) (2021)
- [Tier Balancing: Towards Dynamic Fairness over Underlying Causal Factors](https://mlsanity.com/paper/2301.08987/) (2023)
- [Toward Operationalizing Pipeline-aware ML Fairness: A Research Agenda for Developing Practical Guidelines and Tools](https://mlsanity.com/paper/2309.17337/) (2023)
- [Adapting Static Fairness to Sequential Decision-Making: Bias Mitigation Strategies towards Equal Long-term Benefit Rate](https://mlsanity.com/paper/2309.03426/) (2023)
- [Efficient Algorithms For Fair Clustering with a New Fairness Notion](https://mlsanity.com/paper/2109.00708/) (2021)
- [Fairer LP-based Online Allocation via Analytic Center](https://mlsanity.com/paper/2110.14621/) (2021)
- [Individually Fair Learning with One-Sided Feedback](https://mlsanity.com/paper/2206.04475/) (2022)
- [Fairness and Sequential Decision Making: Limits, Lessons, and Opportunities](https://mlsanity.com/paper/2301.05753/) (2023)
- [Long-Term Fairness Inquiries and Pursuits in Machine Learning: A Survey of Notions, Methods, and Challenges](https://mlsanity.com/paper/2406.06736/) (2024)
- [Sampling a Near Neighbor in High Dimensions -- Who is the Fairest of Them All?](https://mlsanity.com/paper/2101.10905/) (2021)
- [Network Revenue Management with Demand Learning and Fair Resource-Consumption Balancing](https://mlsanity.com/paper/2207.11159/) (2022)
- [It's Not Fairness, and It's Not Fair: The Failure of Distributional Equality and the Promise of Relational Equality in Complete-Information Hiring Games](https://mlsanity.com/paper/2209.05602/) (2022)
- [AI-Driven Healthcare: A Review on Ensuring Fairness and Mitigating Bias](https://mlsanity.com/paper/2407.19655/) (2024)
- [Fairness in Contextual Resource Allocation Systems: Metrics and Incompatibility Results](https://mlsanity.com/paper/2212.01725/) (2022)
- [Counting Hours, Counting Losses: The Toll of Unpredictable Work Schedules on Financial Security](https://mlsanity.com/paper/2504.07719/) (2025)
- [Fair Allocation in Dynamic Mechanism Design](https://mlsanity.com/paper/2406.00147/) (2024)
- [Resource-constrained Fairness](https://mlsanity.com/paper/2406.01290/) (2024)
- [Online Fair Allocation of Perishable Resources](https://mlsanity.com/paper/2406.02402/) (2024)
- [Fair Resource Allocation for Demands with Sharp Lower Tail Inequalities](https://mlsanity.com/paper/2101.12403/) (2021)
- [Price of Fairness in Short-Term and Long-Term Algorithmic Selections](https://mlsanity.com/paper/2605.06227/) (2026)
- [Trustworthy Data- and ML-Ops for Intelligent Transportation Systems and Logistics](https://mlsanity.com/paper/2610.01282/) (2026)

## Abstract (arXiv)

Settings such as lending and policing can be modeled by a centralized agent allocating a resource (loans or police officers) amongst several groups, in order to maximize some objective (loans given that are repaid or criminals that are apprehended). Often in such problems fairness is also a concern. A natural notion of fairness, based on general principles of equality of opportunity, asks that conditional on an individual being a candidate for the resource, the probability of actually receiving it is approximately independent of the individual's group. In lending this means that equally creditworthy individuals in different racial groups have roughly equal chances of receiving a loan. In policing it means that two individuals committing the same crime in different districts would have roughly equal chances of being arrested. We formalize this fairness notion for allocation problems and investigate its algorithmic consequences. Our main technical results include an efficient learning algorithm that converges to an optimal fair allocation even when the frequency of candidates (creditworthy individuals or criminals) in each group is unknown. The algorithm operates in a censored feedback model in which only the number of candidates who received the resource in a given allocation can be observed, rather than the true number of candidates. This models the fact that we do not learn the creditworthiness of individuals we do not give loans to nor learn about crimes committed if the police presence in a district is low. As an application of our framework, we consider the predictive policing problem. The learning algorithm is trained on arrest data gathered from its own deployments on previous days, resulting in a potential feedback loop that our algorithm provably overcomes. We empirically investigate the performance of our algorithm on the Philadelphia Crime Incidents dataset.