# Long-term Fairness with Selective Labels

arXiv: https://arxiv.org/abs/2605.22291 · HTML: https://mlsanity.com/paper/2605.22291/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 52 references that are in the map.
- First posted on arXiv 21 May 2026.

## Builds on (most cited first, 30 of 36)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Fairness in Criminal Justice Risk Assessments: The State of the Art](https://mlsanity.com/paper/1703.09207/) (2017)
- [Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks](https://mlsanity.com/paper/1703.02930/) (2017)
- [Delayed Impact of Fair Machine Learning](https://mlsanity.com/paper/1803.04383/) (2018)
- [Runaway Feedback Loops in Predictive Policing](https://mlsanity.com/paper/1706.09847/) (2017)
- [Fairness in Reinforcement Learning](https://mlsanity.com/paper/1611.03071/) (2016)
- [How Do Fair Decisions Fare in Long-term Qualification?](https://mlsanity.com/paper/2010.11300/) (2020)
- [Algorithms for Fairness in Sequential Decision Making](https://mlsanity.com/paper/1901.08568/) (2019)
- [Causal Modeling for Fairness in Dynamical Systems](https://mlsanity.com/paper/1909.09141/) (2019)
- [Fair Contextual Multi-Armed Bandits: Theory and Experiments](https://mlsanity.com/paper/1912.08055/) (2019)
- [Equal Opportunity in Online Classification with Partial Feedback](https://mlsanity.com/paper/1902.02242/) (2019)
- [Achieving Long-Term Fairness in Sequential Decision Making](https://mlsanity.com/paper/2204.01819/) (2022)
- [Policy Optimization with Advantage Regularization for Long-Term Fairness in Decision Systems](https://mlsanity.com/paper/2210.12546/) (2022)
- [Towards Return Parity in Markov Decision Processes](https://mlsanity.com/paper/2111.10476/) (2021)
- [Don't Throw it Away! The Utility of Unlabeled Data in Fair Decision Making](https://mlsanity.com/paper/2205.04790/) (2022)
- [Efficient Resource Allocation with Fairness Constraints in Restless Multi-Armed Bandits](https://mlsanity.com/paper/2206.03883/) (2022)
- [Fair Off-Policy Learning from Observational Data](https://mlsanity.com/paper/2303.08516/) (2023)
- [Online Restless Multi-Armed Bandits with Long-Term Fairness Constraints](https://mlsanity.com/paper/2312.10303/) (2023)
- [Designing Long-term Group Fair Policies in Dynamical Systems](https://mlsanity.com/paper/2311.12447/) (2023)
- [Automating Data Annotation under Strategic Human Agents: Risks and Potential Solutions](https://mlsanity.com/paper/2405.08027/) (2024)
- [Remembering to Be Fair: Non-Markovian Fairness in Sequential Decision Making](https://mlsanity.com/paper/2312.04772/) (2023)
- [The Fragility of Fairness: Causal Sensitivity Analysis for Fair Machine Learning](https://mlsanity.com/paper/2410.09600/) (2024)
- [Adapting Static Fairness to Sequential Decision-Making: Bias Mitigation Strategies towards Equal Long-term Benefit Rate](https://mlsanity.com/paper/2309.03426/) (2023)
- [Algorithmic Fairness in Performative Policy Learning: Escaping the Impossibility of Group Fairness](https://mlsanity.com/paper/2405.20447/) (2024)
- [Striking a Balance in Fairness for Dynamic Systems Through Reinforcement Learning](https://mlsanity.com/paper/2401.06318/) (2024)
- [Long-Term Fairness Inquiries and Pursuits in Machine Learning: A Survey of Notions, Methods, and Challenges](https://mlsanity.com/paper/2406.06736/) (2024)

## Abstract (arXiv)

Long-term fairness algorithms aim to satisfy fairness beyond static and short-term notions by accounting for the dynamics between decision-making policies and population behavior. Most previous approaches evaluate performance and fairness measures from observable features and a label, which is assumed to be fully observed. However, in scenarios such as hiring or lending, the labels (e.g., ability to repay the loan) are selective labels as they are only revealed based on positive decisions (e.g., when a loan is granted). In this paper, we study long-term fairness in the selective labels setting and analytically show that naive solutions do not guarantee fairness. To address this gap, we then introduce a novel framework that leverages both the observed data and a label predictor model to estimate the true fairness measure value by decomposing it into the observed fairness and bias from label predictions. This allows us to derive sufficient conditions to satisfy true fairness from observable quantities by using the confidence in the predictor model. Finally, we rely on our theoretical results to propose a novel reinforcement learning algorithm for effective long-term fair decision-making with selective labels. In semisynthetic environments, the proposed algorithm reached comparable fairness and performance to an agent with oracle access to the true labels.