Learning-Augmented Facility Location Mechanisms for the Envy Ratio Objective

2025-12-11

AI Summary

This paper studies envy-ratio fairness—minimizing the maximum utility ratio between any two agents—in one-dimensional facility location. It introduces, for the first time, learning-augmented mechanism design for this objective, proposing a novel framework balancing prediction consistency and robustness. Methodologically, it integrates combinatorial mechanism design, randomized techniques, and machine learning–based prediction integration. Theoretical contributions include: (1) resolving an open problem posed by Ding et al. on optimal deterministic mechanisms, establishing tight bounds of α-consistency and α/(α−1)-robustness for α ∈ [1,2]; (2) constructing the first prediction-augmented randomized mechanism, improving the worst-case approximation ratio from 2 (without predictions) to 1.8944; and (3) surpassing fundamental performance trade-off barriers when predictions are available. The work establishes new theoretical foundations and practical tools for fair facility location.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Machine Learning: Learning Preferences or Rankings

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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 $αin [1,2]$, 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.

Problem

• Design learning-augmented mechanisms for facility location on a line
• Optimize fairness via envy ratio objective using predictions
• Achieve consistency and robustness bounds with deterministic and randomized approaches

Innovation

• Learning-augmented mechanisms for envy ratio objective
• Deterministic mechanism with consistency and robustness guarantees
• Randomized mechanism improving approximation ratio using predictions