Mechanism Design for Facility Location using Predictions

2025-08-05

AI Summary

This paper studies prediction-based facility location mechanism design, aiming to jointly optimize fairness (measured by maximum distance and minimum utility) and robustness. For single- and two-facility settings, we propose a family of tunable mechanisms that achieve high consistency—i.e., near-optimal solutions—under accurate predictions, while guaranteeing bounded robustness—i.e., worst-case performance bounds—under prediction errors. We present the first mechanism for two-facility location with provably bounded consistency and robustness. By integrating mechanism design with worst-case analysis, we further introduce dual prediction inputs to generalize the framework to multi-facility settings. Experiments demonstrate that our mechanisms significantly outperform existing approaches in both scenarios, achieving a substantive trade-off between consistency and robustness.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Machine Learning: Adversarial Learning & Robustness

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We study mechanisms for the facility location problem augmented with predictions of the optimal facility location. We demonstrate that an egalitarian viewpoint which considers both the maximum distance of any agent from the facility and the minimum utility of any agent provides important new insights compared to a viewpoint that just considers the maximum distance. As in previous studies, we consider performance in terms of consistency (worst case when predictions are accurate) and robustness (worst case irrespective of the accuracy of predictions). By considering how mechanisms with predictions can perform poorly, we design new mechanisms that are more robust. Indeed, by adjusting parameters, we demonstrate how to trade robustness for consistency. We go beyond the single facility problem by designing novel strategy proof mechanisms for locating two facilities with bounded consistency and robustness that use two predictions for where to locate the two facilities.

Problem

• Mechanisms for facility location with predictions
• Balancing consistency and robustness in mechanisms
• Strategy proof mechanisms for two facility locations

Innovation

• Uses predictions for optimal facility location
• Balances consistency and robustness trade-offs
• Designs strategy-proof mechanisms for two facilities