Linear Program-Based Approximation for Personalized Reserve Prices
针对无假设估值分布下的个性化保留价优化问题，提出线性规划与舍入方法，实现0.684近似比，优于现有算法，适用于在线广告等拍卖场景。
We study the problem of computing data-driven personalized reserve prices in eager second price auctions without having any assumption on valuation distributions. Here, the input is a data set that contains the submitted bids of n buyers in a set of auctions, and the problem is to return personalized reserve prices r that maximize the revenue earned on these auctions by running eager second price auctions with reserve r. For this problem, which is known to be NP complete, we present a novel linear program (LP) formulation and a rounding procedure, which achieves a 0.684 approximation. This improves over the [Formula: see text]-approximation algorithm from Roughgarden and Wang. We show that our analysis is tight for this rounding procedure. We also bound the integrality gap of the LP, which shows that it is impossible to design an algorithm that yields an approximation factor larger than 0.828 with respect to this LP. This paper was accepted by Chung Piaw Teo, Management Science Special Section on Data-Driven Prescriptive Analytics.