# Online Multi-Class Selection with Group Fairness Guarantee

arXiv: https://arxiv.org/abs/2510.21055 · HTML: https://mlsanity.com/paper/2510.21055/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 49 references that are in the map.
- First posted on arXiv 23 Oct 2025.

## Builds on (most cited first, 26 of 26)

- [Proportionally Fair Clustering](https://mlsanity.com/paper/1905.03674/) (2019)
- [Improving Online Algorithms via ML Predictions](https://mlsanity.com/paper/2407.17712/) (2024)
- [Optimal Robustness-Consistency Trade-offs for Learning-Augmented Online Algorithms](https://mlsanity.com/paper/2010.11443/) (2020)
- [Pareto-Optimal Learning-Augmented Algorithms for Online Conversion Problems](https://mlsanity.com/paper/2109.01556/) (2021)
- [Online Nash Social Welfare Maximization with Predictions](https://mlsanity.com/paper/2008.03564/) (2020)
- [Competitive Algorithms for the Online Multiple Knapsack Problem with Application to Electric Vehicle Charging](https://mlsanity.com/paper/2010.00412/) (2020)
- [Online Conversion with Switching Costs: Robust and Learning-Augmented Algorithms](https://mlsanity.com/paper/2310.20598/) (2023)
- [Single-Leg Revenue Management with Advice](https://mlsanity.com/paper/2202.10939/) (2022)
- [Proportionally Fair Online Allocation of Public Goods with Predictions](https://mlsanity.com/paper/2209.15305/) (2022)
- [No-regret Algorithms for Fair Resource Allocation](https://mlsanity.com/paper/2303.06396/) (2023)
- [Optimal Posted Prices for Online Cloud Resource Allocation](https://mlsanity.com/paper/1704.05511/) (2017)
- [Edge-Weighted Online Bipartite Matching](https://mlsanity.com/paper/2005.01929/) (2020)
- [Approximate Group Fairness for Clustering](https://mlsanity.com/paper/2203.17146/) (2022)
- [Proportional Fairness in Non-Centroid Clustering](https://mlsanity.com/paper/2410.23273/) (2024)
- [Class Fairness in Online Matching](https://mlsanity.com/paper/2203.03751/) (2022)
- [Adwords in a Panorama](https://mlsanity.com/paper/2009.04114/) (2020)
- [Online Nash Welfare Maximization Without Predictions](https://mlsanity.com/paper/2211.03077/) (2022)
- [Chasing Convex Functions with Long-term Constraints](https://mlsanity.com/paper/2402.14012/) (2024)
- [Fair Secretaries with Unfair Predictions](https://mlsanity.com/paper/2411.09854/) (2024)
- [Multi-model Online Conformal Prediction with Graph-Structured Feedback](https://mlsanity.com/paper/2506.20898/) (2025)
- [Tight Bounds for Online Edge Coloring](https://mlsanity.com/paper/1904.09222/) (2019)
- [Threshold Policies with Tight Guarantees for Online Selection with Convex Costs](https://mlsanity.com/paper/2310.06166/) (2023)
- [Randomized Rounding Approaches to Online Allocation, Sequencing, and Matching](https://mlsanity.com/paper/2407.20419/) (2024)
- [Fairness and Efficiency in Online Class Matching](https://mlsanity.com/paper/2410.19163/) (2024)
- [Online Allocation with Multi-Class Arrivals: Group Fairness vs Individual Welfare](https://mlsanity.com/paper/2501.15782/) (2025)
- [Online Rounding Schemes for  k -Rental Problems](https://mlsanity.com/paper/2507.19649/) (2025)

## Abstract (arXiv)

We study the online multi-class selection problem with group fairness guarantees, where limited resources must be allocated to sequentially arriving agents. Our work addresses two key limitations in the existing literature. First, we introduce a novel lossless rounding scheme that ensures the integral algorithm achieves the same expected performance as any fractional solution. Second, we explicitly address the challenges introduced by agents who belong to multiple classes. To this end, we develop a randomized algorithm based on a relax-and-round framework. The algorithm first computes a fractional solution using a resource reservation approach -- referred to as the set-aside mechanism -- to enforce fairness across classes. The subsequent rounding step preserves these fairness guarantees without degrading performance. Additionally, we propose a learning-augmented variant that incorporates untrusted machine-learned predictions to better balance fairness and efficiency in practical settings.