Mechanism Design for Facility Location using Predictions

TL;DR

This paper introduces new mechanism design strategies for facility location problems that incorporate predictions, balancing robustness and consistency, and extends to multiple facilities with strategy-proof mechanisms.

Contribution

It proposes a novel egalitarian approach considering both maximum distance and minimum utility, and designs strategy-proof mechanisms for locating multiple facilities using predictions.

Findings

Mechanisms with predictions can be tuned for robustness and consistency.

New strategy-proof mechanisms for two-facility location using predictions.

Enhanced understanding of the trade-offs in mechanism performance.

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.