Procurement Auctions with Predictions: Improved Frugality for Facility Location

TL;DR

This work studies truthful procurement auctions for the strategic uncapacitated facility location problem, balancing facility opening costs and customer connection costs. It first proves a tight frugality bound of 3 for the VCG auction and then introduces learning-augmented mechanisms that leverage cost predictions to dramatically reduce payments when predictions are accurate, while remaining robust to prediction errors. The PredictedLimits mechanism achieves $(1+\epsilon)$-consistency with a robustness bound of $\max\{5,3+2/\epsilon\}$, and the ErrorTolerant variant offers a finer tradeoff characterized by the prediction error $\eta$ and a tolerance parameter $\lambda$, achieving $\eta(1+\lambda)+2\epsilon$ when $\eta\le\lambda$ and a constant-robustness bound otherwise. Collectively, the results advance frugal mechanism design in a learning-augmented, prediction-aware setting for strategic facility location, with implications for procurement auctions and public sector bidding where cost predictions are informally available from data-driven models.

Abstract

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.

Figures (2)

• Figure 1: Illustration of how users in $U_{\ell,f}$ are rerouted to facility $\pi_f(\ell)$. Each color (and line pattern) denotes the path taken by a distinct user $u \in U_{\ell,f}$. The total connection‐cost along each set of colored edges gives an upper bound on the payment to facility $\ell$ for serving that subset of users.
• Figure 2: Illustration of the lower bound instance where each square represents a facility location with its opening cost, and the circles represent users.

Theorems & Definitions (46)

• Lemma 2.1: Myerson’s Lemma
• Lemma 3.1: Unified payment bound under set-dependent scaling
• proof : Proof of Lemma \ref{['lem:unified-wprime']}
• Corollary 3.2
• proof
• Lemma 3.3
• proof
• Theorem 3.4
• Theorem 4.1
• Lemma 4.2