Randomized Strategic Facility Location with Predictions

TL;DR

This paper investigates randomized truthful mechanisms for strategic facility location problems, analyzing how different predictions and randomization improve approximation of optimal social costs in various metric spaces.

Contribution

It introduces randomized mechanisms and explores the effects of various prediction types, advancing understanding beyond deterministic approaches in strategic facility location.

Findings

Randomization improves approximation bounds in strategic facility location.

Different prediction types significantly impact mechanism performance.

Bounds established for approximation ratios in single-dimensional and Euclidean spaces.

Abstract

In the strategic facility location problem, a set of agents report their locations in a metric space and the goal is to use these reports to open a new facility, minimizing an aggregate distance measure from the agents to the facility. However, agents are strategic and may misreport their locations to influence the facility's placement in their favor. The aim is to design truthful mechanisms, ensuring agents cannot gain by misreporting. This problem was recently revisited through the learning-augmented framework, aiming to move beyond worst-case analysis and design truthful mechanisms that are augmented with (machine-learned) predictions. The focus of this prior work was on mechanisms that are deterministic and augmented with a prediction regarding the optimal facility location. In this paper, we provide a deeper understanding of this problem by exploring the power of randomization as well as the impact of different types of predictions on the performance of truthful learning-augmented mechanisms. We study both the single-dimensional and the Euclidean case and provide upper and lower bounds regarding the achievable approximation of the optimal egalitarian social cost.