Large Language Models for Multi-Facility Location Mechanism Design

• URL: http://arxiv.org/abs/2503.09533v2
• Date: Thu, 13 Mar 2025 05:54:22 GMT
• Title: Large Language Models for Multi-Facility Location Mechanism Design
• Authors: Nguyen Thach, Fei Liu, Houyu Zhou, Hau Chan,
• Abstract summary: Deep learning models have been proposed as alternatives to strategyproof mechanisms for multi-facility location.<n>We introduce a novel approach, named LLMMech, that addresses these limitations by incorporating large language models into an evolutionary framework.<n>Our experimental results, evaluated on various problem settings, demonstrate that the LLM-generated mechanisms generally outperform existing handcrafted baselines and deep learning models.
• Score: 16.88708405619343
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Designing strategyproof mechanisms for multi-facility location that optimize social costs based on agent preferences had been challenging due to the extensive domain knowledge required and poor worst-case guarantees. Recently, deep learning models have been proposed as alternatives. However, these models require some domain knowledge and extensive hyperparameter tuning as well as lacking interpretability, which is crucial in practice when transparency of the learned mechanisms is mandatory. In this paper, we introduce a novel approach, named LLMMech, that addresses these limitations by incorporating large language models (LLMs) into an evolutionary framework for generating interpretable, hyperparameter-free, empirically strategyproof, and nearly optimal mechanisms. Our experimental results, evaluated on various problem settings where the social cost is arbitrarily weighted across agents and the agent preferences may not be uniformly distributed, demonstrate that the LLM-generated mechanisms generally outperform existing handcrafted baselines and deep learning models. Furthermore, the mechanisms exhibit impressive generalizability to out-of-distribution agent preferences and to larger instances with more agents.

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