# Fairness in Reinforcement Learning

arXiv: https://arxiv.org/abs/1611.03071 · HTML: https://mlsanity.com/paper/1611.03071/

## Key facts

- Cited by 95 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Nov 2016.

## Built on by (most cited first, 30 of 95)

- [Harms from Increasingly Agentic Algorithmic Systems](https://mlsanity.com/paper/2302.10329/) (2023)
- [A Clarification of the Nuances in the Fairness Metrics Landscape](https://mlsanity.com/paper/2106.00467/) (2021)
- [Datasets and Benchmarks for Offline Safe Reinforcement Learning](https://mlsanity.com/paper/2306.09303/) (2023)
- [Trustworthy Reinforcement Learning Against Intrinsic Vulnerabilities: Robustness, Safety, and Generalizability](https://mlsanity.com/paper/2209.08025/) (2022)
- [Evaluating Fairness of Machine Learning Models Under Uncertain and Incomplete Information](https://mlsanity.com/paper/2102.08410/) (2021)
- [A Simple Reward-free Approach to Constrained Reinforcement Learning](https://mlsanity.com/paper/2107.05216/) (2021)
- [Fairness in Recommendation: Foundations, Methods and Applications](https://mlsanity.com/paper/2205.13619/) (2022)
- [Long-Term Fairness with Unknown Dynamics](https://mlsanity.com/paper/2304.09362/) (2023)
- [A Sociotechnical View of Algorithmic Fairness](https://mlsanity.com/paper/2110.09253/) (2021)
- [Online certification of preference-based fairness for personalized recommender systems](https://mlsanity.com/paper/2104.14527/) (2021)
- [When Fair Ranking Meets Uncertain Inference](https://mlsanity.com/paper/2105.02091/) (2021)
- [Welfare and Fairness in Multi-objective Reinforcement Learning](https://mlsanity.com/paper/2212.01382/) (2022)
- [Achieving Long-Term Fairness in Sequential Decision Making](https://mlsanity.com/paper/2204.01819/) (2022)
- [Unintended Selection: Persistent Qualification Rate Disparities and Interventions](https://mlsanity.com/paper/2111.01201/) (2021)
- [What-is and How-to for Fairness in Machine Learning: A Survey, Reflection, and Perspective](https://mlsanity.com/paper/2206.04101/) (2022)
- [Fair Sequential Selection Using Supervised Learning Models](https://mlsanity.com/paper/2110.13986/) (2021)
- [FaiR-IoT: Fairness-aware Human-in-the-Loop Reinforcement Learning for Harnessing Human Variability in Personalized IoT](https://mlsanity.com/paper/2103.16033/) (2021)
- [Achieving Counterfactual Fairness for Causal Bandit](https://mlsanity.com/paper/2109.10458/) (2021)
- [Multi-dimensional discrimination in Law and Machine Learning -- A comparative overview](https://mlsanity.com/paper/2302.05995/) (2023)
- [Survey on Fair Reinforcement Learning: Theory and Practice](https://mlsanity.com/paper/2205.10032/) (2022)
- [Towards Return Parity in Markov Decision Processes](https://mlsanity.com/paper/2111.10476/) (2021)
- [Socially Fair Reinforcement Learning](https://mlsanity.com/paper/2208.12584/) (2022)
- [Fair Off-Policy Learning from Observational Data](https://mlsanity.com/paper/2303.08516/) (2023)
- [Fairness with Continuous Optimal Transport](https://mlsanity.com/paper/2101.02084/) (2021)
- [Recommendation Fairness: From Static to Dynamic](https://mlsanity.com/paper/2109.03150/) (2021)
- [Reinforcement Learning with Stepwise Fairness Constraints](https://mlsanity.com/paper/2211.03994/) (2022)
- [Fairness in Preference-based Reinforcement Learning](https://mlsanity.com/paper/2306.09995/) (2023)
- [Designing Long-term Group Fair Policies in Dynamical Systems](https://mlsanity.com/paper/2311.12447/) (2023)
- [Fairness in Reinforcement Learning: A Survey](https://mlsanity.com/paper/2405.06909/) (2024)
- [Cooperative Multi-Agent Fairness and Equivariant Policies](https://mlsanity.com/paper/2106.05727/) (2021)

## Abstract (arXiv)

We initiate the study of fairness in reinforcement learning, where the actions of a learning algorithm may affect its environment and future rewards. Our fairness constraint requires that an algorithm never prefers one action over another if the long-term (discounted) reward of choosing the latter action is higher. Our first result is negative: despite the fact that fairness is consistent with the optimal policy, any learning algorithm satisfying fairness must take time exponential in the number of states to achieve non-trivial approximation to the optimal policy. We then provide a provably fair polynomial time algorithm under an approximate notion of fairness, thus establishing an exponential gap between exact and approximate fairness