Strategyproof Mechanisms for Facility Location with Prediction Under the Maximum Cost Objective

2025-08-30

AI Summary

This paper studies the facility location mechanism design problem in metric spaces with learning-augmented predictions, aiming to design strategyproof (SP) mechanisms that minimize the maximum agent cost under truthful reporting, leveraging imperfect predictions. It introduces, for the first time in this setting, the dual desiderata of *consistency*—improved approximation ratio when predictions are accurate—and *robustness*—preservation of the optimal worst-case guarantee regardless of prediction error. The authors propose a deterministic mechanism, MinMaxP. On the real line, MinMaxP achieves a tight (1 + min{1, η})-approximation ratio, where η quantifies prediction error. They extend MinMaxP to two-dimensional ℓₚ spaces and analyze its group-strategyproofness. The theoretical analysis integrates tools from mechanism design and metric geometry, addressing both deterministic and randomized mechanisms. This work establishes the first optimal framework for learning-augmented mechanism design that simultaneously achieves consistency and robustness.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions

Abstract

We study the mechanism design problem of facility location on a metric space in the learning-augmented framework, where mechanisms have access to an imperfect prediction of optimal facility locations. Our goal is to design strategyproof (SP) mechanisms to elicit agent preferences on the facility locations truthfully and, leveraging the given imperfect prediction, determine the facility location that approximately minimizes the maximum cost among all agents. In particular, we seek SP mechanisms whose approximation guarantees depend on the prediction errors -- achieve improved guarantees when the prediction is accurate (known as the emph{consistency}), while still ensuring robust worst-case performance when the prediction is arbitrarily inaccurate (known as the emph{robustness}). When the metric space is the real line, we characterize all deterministic SP mechanisms with consistency strictly less than 2 and bounded robustness: such mechanisms must be the MinMaxP mechanism, which returns the prediction location if it lies between the two extreme agent locations and, otherwise, returns the closest agent location to the prediction. We further show that, for any prediction error $ηge 0$, while MinMaxP is $(1+min(1, η))$-approximation, no deterministic SP mechanism can achieve a better approximation. In two-dimensional spaces with the $l_p$ metric, we analyze the approximation guarantees of a deterministic mechanism that runs MinMaxP independently on each coordinate, as well as a randomized mechanism that selects between two deterministic ones with specific probabilities. Finally, we discuss the group strategyproofness of the considered mechanisms.

Problem

• Designing strategyproof mechanisms for facility location with predictions
• Achieving improved consistency when predictions are accurate
• Ensuring robustness against arbitrarily inaccurate predictions

Innovation

• Strategyproof mechanisms with imperfect predictions
• MinMaxP mechanism for real line metrics
• Coordinate-wise and randomized methods for 2D spaces