Optimal Learning-Augmented Algorithm for Online Bidding

TL;DR

This paper introduces a Pareto-optimal randomized learning-augmented algorithm for online bidding, utilizing a novel bidding profile framework to optimize the trade-off between robustness and consistency.

Contribution

It presents a new framework for representing randomized algorithms via bidding profiles and characterizes the optimal profile through differential equations, closing existing bounds gaps.

Findings

Developed a Pareto-optimal randomized algorithm for online bidding.

Introduced the bidding profile framework for representing bid distributions.

Extended the approach to linear search, improving prior algorithms.

Abstract

Recent advances in machine learning have spurred significant interest in learning-augmented algorithms, particularly for online optimization. A growing body of work has studied online bidding in this framework, aiming to characterize the trade-off between robustness and consistency. While this trade-off is fully understood for deterministic algorithms, a gap between upper and lower bounds remains in the randomized setting. In this paper, we close this gap by presenting a Pareto-optimal randomized learning-augmented algorithm for this problem. Our approach introduces the notion of a bidding profile, a novel framework for representing the distribution over bids generated by an algorithm. We show that any bidding algorithm can be reduced, without loss of generality, to one driven by a bidding profile, and we characterize the optimal profile via a system of delayed differential equations. Finally, we demonstrate the broader applicability of our approach by extending it to the linear search problem, yielding a significant improvement over prior learning-augmented algorithms for linear search.