Many online advertising platforms provide advertisers with auto-bidding services to enhance their advertising performance. However, most existing auto-bidding algorithms fail to accurately capture the auto-bidding problem formulation that the platform truly faces, let alone solve it. Actually, we argue that the platform should try to help optimize each advertiser's performance to the greatest extent -- which makes $\epsilon$-Nash Equilibrium ($\epsilon$-NE) a necessary solution concept -- while maximizing the social welfare of all the advertisers for the platform's long-term value. Based on this, we introduce the \emph{Nash-Equilibrium Constrained Bidding} (NCB), a new formulation of the auto-bidding problem from the platform's perspective. Specifically, it aims to maximize the social welfare of all advertisers under the $\epsilon$-NE constraint. However, the NCB problem presents significant challenges due to its constrained bi-level structure and the typically large number of advertisers involved. To address these challenges, we propose a \emph{Bi-level Policy Gradient} (BPG) framework with theoretical guarantees. Notably, its computational complexity is independent of the number of advertisers, and the associated gradients are straightforward to compute. Extensive simulated and real-world experiments validate the effectiveness of the BPG framework.

本研究针对现有自动出价算法未能准确捕捉在线广告平台所面临的自动出价问题，提出了一种新的自动出价问题表述——纳什均衡约束出价（NCB），旨在最大化广告商的社会福利同时满足$\epsilon$-纳什均衡约束。通过引入具有理论保证的双层策略梯度（BPG）框架，本研究克服了NCB问题的复杂性，其计算复杂度与广告商数量无关，实验验证了其有效性。

纳什均衡约束的自动出价与双层强化学习