Online Multi-Class Selection with Group Fairness Guarantee

2025-10-23

AI Summary

This paper studies the online multi-category selection problem under resource constraints and adversarial arrival of requesters, with the objective of ensuring group fairness. To address two key limitations of prior work—(i) the absence of lossless rounding mechanisms to match the expected performance of fractional solutions, and (ii) the difficulty in handling individuals belonging to multiple categories—we propose the first lossless randomized rounding framework, guaranteeing that the integral algorithm achieves the same expected performance as the optimal fractional solution. Methodologically, we integrate the relaxation-and-rounding paradigm with dynamic resource reservation and untrusted machine learning predictions to enable efficient, fairness-constrained decision-making. We provide theoretical guarantees establishing strict group fairness and optimal expected performance. Empirical evaluations demonstrate that learning-augmented components significantly improve practical utility.

Technology Category

• Machine Learning: Online Learning & Bandits
• Game Theory and Economic Paradigms: Fair Division
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Ensures group fairness in online multi-class resource allocation
• Develops lossless rounding for integral algorithm matching fractional performance
• Addresses overlapping class membership challenges with relax-and-round framework

Innovation

• Lossless rounding scheme matching fractional solution performance
• Set-aside mechanism ensuring fairness across multiple classes
• Learning-augmented algorithm balancing fairness with predictions