The Pareto Frontier of Randomized Learning-Augmented Online Bidding

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.