# Group Meritocratic Fairness in Linear Contextual Bandits

arXiv: https://arxiv.org/abs/2206.03150 · HTML: https://mlsanity.com/paper/2206.03150/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 42 references that are in the map.
- First posted on arXiv 7 Jun 2022.

## Builds on (most cited first, 20 of 20)

- [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)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [Avoiding Discrimination through Causal Reasoning](https://mlsanity.com/paper/1706.02744/) (2017)
- [Fair Clustering Through Fairlets](https://mlsanity.com/paper/1802.05733/) (2018)
- [Fairness in Learning: Classic and Contextual Bandits](https://mlsanity.com/paper/1605.07139/) (2016)
- [Beyond Parity: Fairness Objectives for Collaborative Filtering](https://mlsanity.com/paper/1705.08804/) (2017)
- [Achieving Fairness in the Stochastic Multi-armed Bandit Problem](https://mlsanity.com/paper/1907.10516/) (2019)
- [Combinatorial Sleeping Bandits with Fairness Constraints](https://mlsanity.com/paper/1901.04891/) (2019)
- [On the relation between accuracy and fairness in binary classification](https://mlsanity.com/paper/1505.05723/) (2015)
- [Calibrated Fairness in Bandits](https://mlsanity.com/paper/1707.01875/) (2017)
- [Fairness of Exposure in Stochastic Bandits](https://mlsanity.com/paper/2103.02735/) (2021)
- [Fair Contextual Multi-Armed Bandits: Theory and Experiments](https://mlsanity.com/paper/1912.08055/) (2019)
- [A statistical framework for fair predictive algorithms](https://mlsanity.com/paper/1610.08077/) (2016)
- [Equal Opportunity in Online Classification with Partial Feedback](https://mlsanity.com/paper/1902.02242/) (2019)
- [Fairness in Learning-Based Sequential Decision Algorithms: A Survey](https://mlsanity.com/paper/2001.04861/) (2020)
- [On preserving non-discrimination when combining expert advice](https://mlsanity.com/paper/1810.11829/) (2018)

## Built on by (most cited first, 9 of 9)

- [Directional Optimism for Safe Linear Bandits](https://mlsanity.com/paper/2308.15006/) (2023)
- [Honor Among Bandits: No-Regret Learning for Online Fair Division](https://mlsanity.com/paper/2407.01795/) (2024)
- [Long-Term Fairness Inquiries and Pursuits in Machine Learning: A Survey of Notions, Methods, and Challenges](https://mlsanity.com/paper/2406.06736/) (2024)
- [Keep Everyone Happy: Online Fair Division of Numerous Items with Few Copies](https://mlsanity.com/paper/2408.12845/) (2024)
- [Fair Best Arm Identification with Fixed Confidence](https://mlsanity.com/paper/2408.17313/) (2024)
- [Improved Regret Bounds for Online Fair Division with Bandit Learning](https://mlsanity.com/paper/2501.07022/) (2025)
- [Simultaneously Achieving Group Exposure Fairness and Within-Group Meritocracy in Stochastic Bandits](https://mlsanity.com/paper/2402.05575/) (2024)
- [A Critical Review of Predominant Bias in Neural Networks](https://mlsanity.com/paper/2502.11031/) (2025)
- [Collaborative Min-Max Regret in Grouped Multi-Armed Bandits](https://mlsanity.com/paper/2506.10313/) (2025)

## Abstract (arXiv)

We study the linear contextual bandit problem where an agent has to select one candidate from a pool and each candidate belongs to a sensitive group. In this setting, candidates' rewards may not be directly comparable between groups, for example when the agent is an employer hiring candidates from different ethnic groups and some groups have a lower reward due to discriminatory bias and/or social injustice. We propose a notion of fairness that states that the agent's policy is fair when it selects a candidate with highest relative rank, which measures how good the reward is when compared to candidates from the same group. This is a very strong notion of fairness, since the relative rank is not directly observed by the agent and depends on the underlying reward model and on the distribution of rewards. Thus we study the problem of learning a policy which approximates a fair policy under the condition that the contexts are independent between groups and the distribution of rewards of each group is absolutely continuous. In particular, we design a greedy policy which at each round constructs a ridge regression estimate from the observed context-reward pairs, and then computes an estimate of the relative rank of each candidate using the empirical cumulative distribution function. We prove that, despite its simplicity and the lack of an initial exploration phase, the greedy policy achieves, up to log factors and with high probability, a fair pseudo-regret of order √dT after T rounds, where d is the dimension of the context vectors. The policy also satisfies demographic parity at each round when averaged over all possible information available before the selection. Finally, we use simulated settings and experiments on the US census data to show that our policy achieves sub-linear fair pseudo-regret also in practice.