We study the problem of designing procurement auctions for the strategic uncapacitated facility location problem: a company needs to procure a set of facility locations in order to serve its customers and each facility location is owned by a strategic agent. Each owner has a private cost for providing access to their facility (e.g., renting it or selling it to the company) and needs to be compensated accordingly. The goal is to design truthful auctions that decide which facilities the company should procure and how much to pay the corresponding owners, aiming to minimize the total cost, i.e., the monetary cost paid to the owners and the connection cost suffered by the customers (their distance to the nearest facility). We evaluate the performance of these auctions using the \emph{frugality ratio}. We first analyze the performance of the classic VCG auction in this context and prove that its frugality ratio is exactly $3$. We then leverage the learning-augmented framework and design auctions that are augmented with predictions regarding the owners' private costs. Specifically, we propose a family of learning-augmented auctions that achieve significant payment reductions when the predictions are accurate, leading to much better frugality ratios. At the same time, we demonstrate that these auctions remain robust even if the predictions are arbitrarily inaccurate, and maintain reasonable frugality ratios even under adversarially chosen predictions. We finally provide a family of ``error-tolerant'' auctions that maintain improved frugality ratios even if the predictions are only approximately accurate, and we provide upper bounds on their frugality ratio as a function of the prediction error.

翻译：本文研究战略性无容量限制设施选址问题的采购拍卖设计：一家公司需采购一组设施选址以服务其客户，每个设施选址由战略性代理拥有。每个所有者提供其设施使用权（如出租或出售给公司）时具有私有成本，需获得相应补偿。目标是设计真实拍卖机制，决定公司应采购哪些设施以及向对应所有者支付多少费用，旨在最小化总成本，即支付给所有者的货币成本与客户承担的连接成本（客户到最近设施的距离）。我们使用\\emph{节俭比率}评估这些拍卖的性能。首先分析经典VCG拍卖在此背景下的表现，证明其节俭比率恰好为$3$。随后利用学习增强框架，设计结合所有者私有成本预测的拍卖机制。具体而言，我们提出一系列学习增强拍卖，当预测准确时可显著降低支付额，从而获得更优的节俭比率。同时证明这些拍卖机制即使在预测完全不准确时仍保持稳健性，在对抗性预测下仍能维持合理的节俭比率。最后提出一类“容错”拍卖机制，即使在预测仅近似准确时仍能保持改进的节俭比率，并给出其节俭比率随预测误差变化的上界。