Learning-Augmented Facility Location Mechanisms for the Envy Ratio Objective
Haris Aziz, Yuhang Guo, Alexander Lam, Houyu Zhou
TL;DR
This paper advances learning-augmented mechanism design for fairness in one-dimensional facility location by analyzing envy-ratio objectives. It introduces a deterministic α-Bounding Interval Mechanism (α-BIM) with tunable consistency-robustness tradeoffs and proves its optimality within deterministic, anonymous, strategyproof mechanisms, while also deriving a prediction-error parameterized bound. It then resolves open questions for randomized mechanisms without predictions, achieving a 1.8944-approximation with an (α,p)-LRM class and providing a new lower bound of 1.12579, and presents a prediction-aware Bias-Aware Mechanism (BAM) that improves both consistency and robustness. Collectively, the work demonstrates the benefits and limits of predictions in envy-ratio fair mechanisms and offers practical design guidelines for learning-augmented fair facility location systems.
Abstract
The augmentation of algorithms with predictions of the optimal solution, such as from a machine-learning algorithm, has garnered significant attention in recent years, particularly in facility location problems. Moving beyond the traditional focus on utilitarian and egalitarian objectives, we design learning-augmented facility location mechanisms on a line for the envy ratio objective, a fairness metric defined as the maximum ratio between the utilities of any two agents. For the deterministic setting, we propose a mechanism which utilizes predictions to achieve $α$-consistency and $\fracα{α- 1}$-robustness for a selected parameter $α\in [1,2]$, and prove its optimality. We also resolve open questions raised by Ding et al. [10], devising a randomized mechanism without predictions to improve upon the best-known approximation ratio from $2$ to $1.8944$. Building upon these advancements, we construct a novel randomized mechanism which incorporates predictions to achieve improved performance guarantees.