Online Allocation with Multi-Class Arrivals: Group Fairness vs Individual Welfare

TL;DR

This paper studies online resource allocation for multiple groups, balancing fairness and efficiency, introduces optimal algorithms, and demonstrates their effectiveness through theoretical analysis and real-world network caching experiments.

Contribution

It develops threshold-based algorithms for multi-class online allocation with fairness guarantees and characterizes the fundamental trade-off between fairness and welfare.

Findings

Optimal algorithms for group fairness in online allocation

Fundamental trade-off between fairness and individual welfare

Empirical validation in network caching scenarios

Abstract

We introduce and study a multi-class online resource allocation problem with group fairness guarantees. The problem involves allocating a fixed amount of resources to a sequence of agents, each belonging to a specific group. The primary objective is to ensure fairness across different groups in an online setting. We focus on three fairness notions: one based on quantity and two based on utility. To achieve fair allocations, we develop two threshold-based online algorithms, proving their optimality under two fairness notions and near-optimality for the more challenging one. Additionally, we demonstrate a fundamental trade-off between group fairness and individual welfare using a novel representative function-based approach. To address this trade-off, we propose a set-aside multi-threshold algorithm that reserves a portion of the resource to ensure fairness across groups while utilizing the remaining resource to optimize efficiency under utility-based fairness notions. This algorithm is proven to achieve the Pareto-optimal trade-off. We also demonstrate that our problem can model a wide range of real-world applications, including network caching and cloud computing, and empirically evaluate our proposed algorithms in the network caching problem using real datasets.