The Pareto Frontier of Randomized Learning-Augmented Online Bidding

TL;DR

This paper analyzes the trade-off between robustness and consistency in randomized online bidding algorithms with predictions, providing tight bounds and a new bidding function framework, supported by practical experiments.

Contribution

It introduces a unified bidding function framework and tight bounds on the robustness-consistency trade-off in randomized learning-augmented online bidding.

Findings

Derived matching upper and lower bounds for the robustness-accuracy trade-off.

Introduced a novel bidding function abstraction for strategy design.

Validated the approach with experiments on the incremental median problem.

Abstract

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.