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

TL;DR

This work studies online resource allocation with multi-class arrivals under group fairness guarantees. It develops threshold-based policies (Q-Threshold, U-Threshold) and a Set-Aside Multi-Threshold scheme (SAM-Threshold) to balance fairness notions—GFQ, $\beta$-PF, and ($\gamma,\beta$)-fairness—and analyzes fundamental trade-offs between group fairness and individual welfare. A representative-function framework provides tight lower bounds, with optimal or near-optimal guarantees for GFQ, $\beta$-PF, and ($\gamma,\beta$)-fairness, including special cases like NSW and MM. The framework is validated on network caching and cloud/TTL caching scenarios using real data, highlighting practical implications for fairness-aware online allocation in systems like caching and cloud computing.

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.

Figures (10)

• Figure 1: Relationship between GFQ, $\beta$-PF, and ($\gamma,\beta$)-fairness. These fairness metrics converge when $\beta = 1$ for $\beta$-PF and ($\gamma,\beta$)-fairness, and when $m_j = \frac{B}{K}$ for GFQ. If $\gamma = 1$, $(\gamma, \beta)$-fairness reduces to $\beta$-NSW.
• Figure 2: Graphical representation of the fairness guarantees achieved by our algorithm for ($\gamma,\beta$)-fairness in Theorem \ref{['theorem-gamma-beta-fairness']} (i.e., upper bound) and the lower-bound results in Theorem \ref{['theorem-gamma-beta-lowerbound']}.
• Figure 3: The fairness guarantee of U-Threshold with ($\gamma,\beta$)-fairness vs lower bound; $\theta_1 = 2$, $\theta_2 = 100$.
• Figure 4: The trade-off between fairness and competitiveness for different values of $\gamma$; $\theta_1 = 2$, $\theta_2 = 100$.
• Figure 5: Results of the first experiment; $\theta_1 = 116$, $\theta_2 = 178$ and $\theta_3 = 253.9$.

Theorems & Definitions (40)

• Definition 1: Group Fairness by Quantity
• Definition 2: $\beta$-Proportional Fairness
• Definition 3: $(\gamma,\beta$)-fairness
• Remark 1: Connection between Fairness Metrics
• Remark 2: Fairness Guarantee $\beta$
• Remark 3: Implications of Efficiency and Fairness Metrics
• Theorem 1: McORA with GFQ Guarantee
• Theorem 2: GFQ Lower Bound
• Theorem 3: $\beta$-PF Guarantee
• Theorem 4: $\beta$-PF Lower-Bound