Optimal Learning-Augmented Algorithm for Online Bidding

2026-05-08

AI Summary

This work addresses the optimal trade-off between robustness and consistency in learning-augmented algorithms for online bidding. The authors propose a Pareto-optimal randomized learning-augmented algorithm that innovatively introduces the notion of a “bidding profile” and characterizes its probability distribution via delayed differential equations. This approach is the first to close the gap between upper and lower bounds for learning-augmented online bidding algorithms under stochastic settings, and it naturally extends to linear search problems. Experimental results demonstrate that the proposed algorithm not only achieves theoretical optimality but also significantly outperforms existing methods on two benchmark tasks.

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.

Problem

• online bidding
• learning-augmented algorithms
• randomized algorithms
• robustness-consistency trade-off
• Pareto optimality

Innovation

• learning-augmented algorithms
• online bidding
• randomized algorithms
• bidding profile
• delayed differential equations