Aiming to overcome some of the limitations of worst-case analysis, the recently proposed framework of "algorithms with predictions" allows algorithms to be augmented with a (possibly erroneous) machine-learned prediction that they can use as a guide. In this framework, the goal is to obtain improved guarantees when the prediction is correct, which is called \emph{consistency}, while simultaneously guaranteeing some worst-case bounds even when the prediction is arbitrarily wrong, which is called \emph{robustness}. The vast majority of the work on this framework has focused on a refined analysis of online algorithms augmented with predictions regarding the future input. A subsequent line of work has also successfully adapted this framework to mechanism design, where the prediction is regarding the private information of strategic agents. In this paper, we initiate the study of online mechanism design with predictions, which combines the challenges of online algorithms with predictions and mechanism design with predictions. We consider the well-studied problem of designing a revenue-maximizing auction to sell a single item to strategic bidders who arrive and depart over time, each with an unknown, private, value for the item. We study the learning-augmented version of this problem where the auction designer is given a prediction regarding the maximum value over all agents. Our main result is a strategyproof mechanism whose revenue guarantees are $\alpha$-consistent with respect to the highest value and $(1-\alpha^2)/4$-robust with respect to the second-highest value, for $\alpha \in [0,1]$. We show that this tradeoff is optimal within a broad and natural family of auctions, meaning that any $\alpha$-consistent mechanism in that family has robustness at most $(1-\alpha^2)/4$. Finally, we extend our mechanism to also achieve expected revenues proportional to the prediction quality.

翻译：旨在克服最坏情况分析的部分局限性，近期提出的"含预测算法"框架允许算法引入（可能错误的）机器学习预测作为指导。在该框架下，目标是在预测正确时获得改进保证（称为一致性），同时即使在预测完全错误时也能保证某些最坏情况边界（称为鲁棒性）。该框架的绝大多数工作聚焦于对加入未来输入预测的在线算法进行精细化分析。后续研究也成功将该框架拓展至机制设计领域，其中预测涉及策略性代理的私人信息。本文首次研究含预测的在线机制设计，该问题融合了含预测在线算法与含预测机制设计的双重挑战。我们考虑经典的收益最大化拍卖设计问题：向随时间到达和离开的策略性投标人出售单一物品，每位投标人对物品具有未知的私人估值。我们研究该问题的学习增强版本，其中拍卖设计者可获得关于所有代理最高估值的预测。主要成果是一个策略防伪机制，其收益保证关于最高估值的α一致性和关于次高估值的(1-α²)/4鲁棒性，其中α∈[0,1]。我们证明该权衡在广泛且自然的拍卖族内是最优的，即该族中任何α一致性机制的鲁棒性至多为(1-α²)/4。最后，我们将机制扩展至实现与预测质量成正比的期望收益。