# Simultaneously Achieving Group Exposure Fairness and Within-Group Meritocracy in Stochastic Bandits

arXiv: https://arxiv.org/abs/2402.05575 · HTML: https://mlsanity.com/paper/2402.05575/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 41 references that are in the map.
- First posted on arXiv 8 Feb 2024.

## Builds on (most cited first, 17 of 17)

- [Fairness in Learning: Classic and Contextual Bandits](https://mlsanity.com/paper/1605.07139/) (2016)
- [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)
- [Online Learning with an Unknown Fairness Metric](https://mlsanity.com/paper/1802.06936/) (2018)
- [Calibrated Fairness in Bandits](https://mlsanity.com/paper/1707.01875/) (2017)
- [Fair clustering via equitable group representations](https://mlsanity.com/paper/2006.11009/) (2020)
- [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)
- [Fair Algorithms for Multi-Agent Multi-Armed Bandits](https://mlsanity.com/paper/2007.06699/) (2020)
- [Group Fairness in Bandit Arm Selection](https://mlsanity.com/paper/1912.03802/) (2019)
- [Combinatorial Multi-armed Bandits for Resource Allocation](https://mlsanity.com/paper/2105.04373/) (2021)
- [Group Meritocratic Fairness in Linear Contextual Bandits](https://mlsanity.com/paper/2206.03150/) (2022)
- [Ballooning Multi-Armed Bandits](https://mlsanity.com/paper/2001.10055/) (2020)
- [Designing Truthful Contextual Multi-Armed Bandits based Sponsored Search Auctions](https://mlsanity.com/paper/2002.11349/) (2020)
- [Max-Min Grouped Bandits](https://mlsanity.com/paper/2111.08862/) (2021)
- [Categorized Bandits](https://mlsanity.com/paper/2005.01656/) (2020)
- [A Novel Demand Response Model and Method for Peak Reduction in Smart Grids -- PowerTAC](https://mlsanity.com/paper/2302.12520/) (2023)

## Built on by (most cited first, 1 of 1)

- [Discrepancy-Rounded Fair Bandits with Static and Time-Varying Exposure Floors](https://mlsanity.com/paper/2607.22935/) (2026)

## Abstract (arXiv)

Existing approaches to fairness in stochastic multi-armed bandits (MAB) primarily focus on exposure guarantee to individual arms. When arms are naturally grouped by certain attribute(s), we propose Bi-Level Fairness, which considers two levels of fairness. At the first level, Bi-Level Fairness guarantees a certain minimum exposure to each group. To address the unbalanced allocation of pulls to individual arms within a group, we consider meritocratic fairness at the second level, which ensures that each arm is pulled according to its merit within the group. Our work shows that we can adapt a UCB-based algorithm to achieve a Bi-Level Fairness by providing (i) anytime Group Exposure Fairness guarantees and (ii) ensuring individual-level Meritocratic Fairness within each group. We first show that one can decompose regret bounds into two components: (a) regret due to anytime group exposure fairness and (b) regret due to meritocratic fairness within each group. Our proposed algorithm BF-UCB balances these two regrets optimally to achieve the upper bound of O(√T) on regret; T being the stopping time. With the help of simulated experiments, we further show that BF-UCB achieves sub-linear regret; provides better group and individual exposure guarantees compared to existing algorithms; and does not result in a significant drop in reward with respect to UCB algorithm, which does not impose any fairness constraint.