# Multi-objective Bandits: Optimizing the Generalized Gini Index

arXiv: https://arxiv.org/abs/1706.04933 · HTML: https://mlsanity.com/paper/1706.04933/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2017.

## Built on by (most cited first, 28 of 28)

- [Promptable Behaviors: Personalizing Multi-Objective Rewards from Human Preferences](https://mlsanity.com/paper/2312.09337/) (2023)
- [Sequential Learning of the Pareto Front for Multi-objective Bandits](https://mlsanity.com/paper/2501.17513/) (2025)
- [Optimizing generalized Gini indices for fairness in rankings](https://mlsanity.com/paper/2204.06521/) (2022)
- [Pareto Regret Analyses in Multi-objective Multi-armed Bandit](https://mlsanity.com/paper/2212.00884/) (2022)
- [Ad-load Balancing via Off-policy Learning in a Content Marketplace](https://mlsanity.com/paper/2309.11518/) (2023)
- [Multi-Objective Recommendation via Multivariate Policy Learning](https://mlsanity.com/paper/2405.02141/) (2024)
- [Fairness in Preference-based Reinforcement Learning](https://mlsanity.com/paper/2306.09995/) (2023)
- [Adapting to Non-Stationary Environments: Multi-Armed Bandit Enhanced Retrieval-Augmented Generation on Knowledge Graphs](https://mlsanity.com/paper/2412.07618/) (2024)
- [No-Regret Learning for Fair Multi-Agent Social Welfare Optimization](https://mlsanity.com/paper/2405.20678/) (2024)
- [Optimal Scalarizations for Sublinear Hypervolume Regret](https://mlsanity.com/paper/2307.03288/) (2023)
- [Provably Efficient Multi-Objective Bandit Algorithms under Preference-Centric Customization](https://mlsanity.com/paper/2502.13457/) (2025)
- [Skill-Aligned Fairness in Multi-Agent Learning for Collaboration in Healthcare](https://mlsanity.com/paper/2508.18708/) (2025)
- [Contextual bandits with concave rewards, and an application to fair ranking](https://mlsanity.com/paper/2210.09957/) (2022)
- [Learning Fair Pareto-Optimal Policies in Multi-Objective Reinforcement Learning](https://mlsanity.com/paper/2606.18111/) (2026)
- [Efficient Online Lexicographic Generalized Low-Rank Matrix Bandits](https://mlsanity.com/paper/2608.04324/) (2026)
- [Multi-thresholding Good Arm Identification with Bandit Feedback](https://mlsanity.com/paper/2503.10386/) (2025)
- [Stochastic Multi-Objective Multi-Armed Bandits: Regret Definition and Algorithm](https://mlsanity.com/paper/2506.13125/) (2025)
- [BanditLP: Large-Scale Stochastic Optimization for Personalized Recommendations](https://mlsanity.com/paper/2601.15552/) (2026)
- [Multi-Objective Multi-Agent Bandits: From Learning Efficiency to Fairness Optimization](https://mlsanity.com/paper/2605.06864/) (2026)
- [Online Pareto-Optimal Decision-Making for Complex Tasks using Active Inference](https://mlsanity.com/paper/2406.11984/) (2024)
- [Procedural Fairness in Multi-Agent Bandits](https://mlsanity.com/paper/2601.10600/) (2026)
- [Are Stochastic Multi-objective Bandits Harder than Single-objective Bandits?](https://mlsanity.com/paper/2604.07096/) (2026)
- [Multi-User Dueling Bandits: A Fair Approach using Nash Social Welfare](https://mlsanity.com/paper/2605.01961/) (2026)
- [Selective Ensemble Based on Preference-Directed Multi-Objective Bandits](https://mlsanity.com/paper/2606.21929/) (2026)
- [Stochastic Primal-Dual Decoding for Multiobjective Generative Recommender Systems](https://mlsanity.com/paper/2607.19357/) (2026)
- [Top-k Pareto Bandits: Hypervolume Regret for Multi-Objective Slate Selection](https://mlsanity.com/paper/2607.26273/) (2026)
- [Inference-Time Policy Alignment for Fair Reinforcement Learning](https://mlsanity.com/paper/2608.00175/) (2026)
- [When More Objectives Make Identification Easier: The Role of Preferences and Feedback](https://mlsanity.com/paper/2610.18577/) (2026)

## Abstract (arXiv)

We study the multi-armed bandit (MAB) problem where the agent receives a vectorial feedback that encodes many possibly competing objectives to be optimized. The goal of the agent is to find a policy, which can optimize these objectives simultaneously in a fair way. This multi-objective online optimization problem is formalized by using the Generalized Gini Index (GGI) aggregation function. We propose an online gradient descent algorithm which exploits the convexity of the GGI aggregation function, and controls the exploration in a careful way achieving a distribution-free regret tildebigO (T-1/2 ) with high probability. We test our algorithm on synthetic data as well as on an electric battery control problem where the goal is to trade off the use of the different cells of a battery in order to balance their respective degradation rates.