Efficient Bid Optimization Method for Budget Constraint Bidding in Online Advertising

With the rapid expansion of digital advertising platforms, online advertising has become a popular business model, facilitating advertisers in reaching potential consumers with personalized ads in real-time. As this trend continues to grow, it raises numerous new research issues, particularly in bid optimization under budget constraints, given its direct impact on advertisers’ benefits. Despite several methods being applied on mainstream platforms over the past decade, efficiency challenges persist. This paper introduces a novel method aimed at reducing time complexity from $O\left(n^{k}\right)$ to $O(n \log n)$, where $k \geq 2$. The initial analysis focuses on understanding the relationship between the bidding formulation and the auction mechanism. Subsequently, the paper demonstrates that the problem can be addressed through sorting, eliminating the need for linear programming, or relying on previous learning methods. Moreover, considering the unknown market uncertainty, a dynamic regret-optimal tracking controller is designed to ensure performance tracking without prior knowledge of disturbances. Finally, experimental evaluations conducted on two open datasets validate the superior performance of the proposed method.