Online Multi-Class Selection with Group Fairness Guarantee

TL;DR

This paper introduces a novel online multi-class selection algorithm with group fairness guarantees, featuring a lossless rounding scheme and a learning-augmented variant to improve fairness and efficiency.

Contribution

It presents a lossless rounding scheme ensuring integral solutions match fractional performance and addresses multi-class overlaps with a relax-and-round framework.

Findings

The algorithm achieves fairness without performance loss.

The set-aside mechanism enforces class fairness.

The learning-augmented variant improves practical efficiency.

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.