Fair Online Resource Allocation

2026-06-17

AI Summary

This study addresses fairness in online resource allocation under sequential agent arrivals and capacity-constrained facilities, with applications ranging from refugee resettlement to flight scheduling. It introduces Lipschitz fairness into this setting for the first time, requiring that agents within the same batch who are similar receive comparable expected allocations. The authors propose an online algorithm based on dual mirror descent that simultaneously satisfies resource constraints, enforces intra-batch fairness, and achieves sublinear regret. Theoretically, they establish that the optimal fair solution attains at least an Ω(1/γ) fraction of the optimal unfair objective value. Empirical validation on real-world data from a refugee economic integration program demonstrates the algorithm’s ability to effectively balance fairness and efficiency.

Abstract

We study the problem of fair online resource allocation, motivated by applications such as refugee resettlement and airline scheduling, where agents arrive sequentially and must be assigned to facilities with limited capacities. We introduce a model that maximizes the overall welfare subject to resource constraints and a Lipschitz fairness requirement, which ensures that similar agents arriving in the same batch receive similar expected outcomes. We first analyze the offline problem, proving that the value of the optimal fair allocation is at least an $Ω(1/γ)$ fraction of the optimal unfair allocation, where $γ$ is the fairness coefficient, thereby bounding the price of fairness. For the online setting, we propose an algorithm based on dual mirror descent that enforces fairness constraints within batches while estimating optimal dual variables. We prove that this algorithm achieves sublinear regret relative to the optimal offline fluid benchmark. Finally, we validate our theoretical results using real-world data from the Refugee Economies Programme, demonstrating the algorithm's performance and examining the trade-offs between welfare maximization and fairness enforcement.

Problem

• fair online resource allocation
• Lipschitz fairness
• sequential arrival
• limited capacities
• fairness-welfare trade-off

Innovation

• fair online allocation
• Lipschitz fairness
• dual mirror descent
• price of fairness
• sublinear regret