Large Language Models for Multi-Facility Location Mechanism Design

TL;DR

The paper tackles incentive-compatible multi-facility location by marrying large language models with an evolutionary search to automatically design interpretable, hyperparameter-free mechanisms that are empirically strategyproof and near-optimal. It formalizes the problem with single-peaked agent preferences, a weighted social-cost objective, and an empirical evaluation framework that penalizes misreporting. The proposed LLMMech framework uses initialization and variation prompts, plus automatic prompt evolution, to generate executable mechanism code and a fitness score guiding search toward low social costs while controlling empirical regret. Empirical results show LLMMech and especially LLMMech-e outperform baselines including neural approaches, with solid generalization to out-of-distribution preferences and larger instance sizes, while maintaining interpretability crucial for policy makers. Overall, the work demonstrates a scalable, transparent approach to mechanism design that reduces manual engineering effort and provides insights into the learned strategies.

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.

Figures (10)

• Figure 1: Representative results for arbitrary weights. Each boxplot records net differences in social cost with respect to LLMMech-e.
• Figure 2: High-level description of a learned mechanism that yields the lowest cost compared to other baselines (2nd row of Table \ref{['tab:res-w-n5+10']}).
• Figure 3: LLM-generated exploration prompt strategy that invokes design of the novel mechanism described in Figure \ref{['fig:learned-mech']}.
• Figure S4: Prompts used for initialization, exploration, and modification. The prompt strategies are marked in purple. See Appendix \ref{['app:code-template']} for the designed "Code Template".
• Figure S5: Prompts used for evolving prompt strategies, where [Type] is 'Exploration' or 'Modification' and X $=|\bm{P}|\le N_p$.

Theorems & Definitions (1)

• Definition 1: Single-peaked preferences