Online bidding is a classical problem in online decision-making, with applications in resource allocation, hierarchical clustering, and the analysis of approximation algorithms. We study its randomized learning-augmented variant, where an online algorithm generates a sequence of random bids while leveraging predictions from an oracle. We provide analytical upper and lower bounds on the optimal consistency $C$ as a function of the robustness $R$, which match when $R \geq 2.885$, effectively closing the gap left by previous work. The key technical ingredient is the notion of a bidding function, a novel abstraction that provides a unified framework for the design and analysis of randomized bidding strategies. We complement our theoretical results with an experimental application of randomized bidding to the incremental median problem, demonstrating the applicability of our algorithm in practical clustering settings.

翻译：在线投标是在线决策中的一个经典问题，在资源分配、层次聚类和近似算法分析中具有广泛应用。我们研究其随机化学习增强变体，其中在线算法在利用来自预言机的预测的同时生成一系列随机投标。我们针对最优一致性$C$（作为鲁棒性$R$的函数）给出了解析上界和下界，这些界在$R \geq 2.885$时相匹配，有效弥合了先前工作留下的差距。关键技术要素是投标函数的概念，这是一种新颖的抽象，为随机化投标策略的设计和分析提供了统一框架。我们通过将随机化投标应用于增量中位数问题的实验应用补充了理论结果，展示了我们的算法在实际聚类场景中的适用性。