# Calibrated Fairness in Bandits

arXiv: https://arxiv.org/abs/1707.01875 · HTML: https://mlsanity.com/paper/1707.01875/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jul 2017.

## Built on by (most cited first, 30 of 43)

- [Trustworthy LLMs: a Survey and Guideline for Evaluating Large Language Models' Alignment](https://mlsanity.com/paper/2308.05374/) (2023)
- [Fairness of Exposure in Stochastic Bandits](https://mlsanity.com/paper/2103.02735/) (2021)
- [Representation Bias in Data: A Survey on Identification and Resolution Techniques](https://mlsanity.com/paper/2203.11852/) (2022)
- [Long-Term Fairness with Unknown Dynamics](https://mlsanity.com/paper/2304.09362/) (2023)
- [Online certification of preference-based fairness for personalized recommender systems](https://mlsanity.com/paper/2104.14527/) (2021)
- [Fair Exploration via Axiomatic Bargaining](https://mlsanity.com/paper/2106.02553/) (2021)
- [What-is and How-to for Fairness in Machine Learning: A Survey, Reflection, and Perspective](https://mlsanity.com/paper/2206.04101/) (2022)
- [Out of Context: Investigating the Bias and Fairness Concerns of "Artificial Intelligence as a Service"](https://mlsanity.com/paper/2302.01448/) (2023)
- [The Pursuit of Fairness in Artificial Intelligence Models: A Survey](https://mlsanity.com/paper/2403.17333/) (2024)
- [Bandit Algorithms for Precision Medicine](https://mlsanity.com/paper/2108.04782/) (2021)
- [Blind Spots and Biases: Exploring the Role of Annotator Cognitive Biases in NLP](https://mlsanity.com/paper/2404.19071/) (2024)
- [An Efficient Algorithm for Fair Multi-Agent Multi-Armed Bandit with Low Regret](https://mlsanity.com/paper/2209.11817/) (2022)
- [Group Meritocratic Fairness in Linear Contextual Bandits](https://mlsanity.com/paper/2206.03150/) (2022)
- [Unmasking Bias in AI: A Systematic Review of Bias Detection and Mitigation Strategies in Electronic Health Record-based Models](https://mlsanity.com/paper/2310.19917/) (2023)
- [Fairness in Reinforcement Learning: A Survey](https://mlsanity.com/paper/2405.06909/) (2024)
- [Multi-disciplinary fairness considerations in machine learning for clinical trials](https://mlsanity.com/paper/2205.08875/) (2022)
- [Fairness-aware Online Price Discrimination with Nonparametric Demand Models](https://mlsanity.com/paper/2111.08221/) (2021)
- [Honor Among Bandits: No-Regret Learning for Online Fair Division](https://mlsanity.com/paper/2407.01795/) (2024)
- [Equitable Restless Multi-Armed Bandits: A General Framework Inspired By Digital Health](https://mlsanity.com/paper/2308.09726/) (2023)
- [Fairer LP-based Online Allocation via Analytic Center](https://mlsanity.com/paper/2110.14621/) (2021)
- [Fairness and Sequential Decision Making: Limits, Lessons, and Opportunities](https://mlsanity.com/paper/2301.05753/) (2023)
- [Holistic Survey of Privacy and Fairness in Machine Learning](https://mlsanity.com/paper/2307.15838/) (2023)
- [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)
- [Network Revenue Management with Demand Learning and Fair Resource-Consumption Balancing](https://mlsanity.com/paper/2207.11159/) (2022)
- [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)
- [Algorithmic Challenges in Ensuring Fairness at the Time of Decision](https://mlsanity.com/paper/2103.09287/) (2021)
- [Fairness Aware Reinforcement Learning via Proximal Policy Optimization](https://mlsanity.com/paper/2502.03953/) (2025)
- [Improving Fairness in Adaptive Social Exergames via Shapley Bandits](https://mlsanity.com/paper/2302.09298/) (2023)

## Abstract (arXiv)

We study fairness within the stochastic, multi-armed bandit (MAB) decision making framework. We adapt the fairness framework of "treating similar individuals similarly" to this setting. Here, an `individual' corresponds to an arm and two arms are `similar' if they have a similar quality distribution. First, we adopt a em smoothness constraint that if two arms have a similar quality distribution then the probability of selecting each arm should be similar. In addition, we define the em fairness regret, which corresponds to the degree to which an algorithm is not calibrated, where perfect calibration requires that the probability of selecting an arm is equal to the probability with which the arm has the best quality realization. We show that a variation on Thompson sampling satisfies smooth fairness for total variation distance, and give an tildeO((kT)2/3) bound on fairness regret. This complements prior work, which protects an on-average better arm from being less favored. We also explain how to extend our algorithm to the dueling bandit setting.