Automated bidding, an emerging intelligent decision making paradigm powered by machine learning, has become popular in online advertising. Advertisers in automated bidding evaluate the cumulative utilities and have private financial constraints over multiple ad auctions in a long-term period. Based on these distinct features, we consider a new ad auction model for automated bidding: the values of advertisers are public while the financial constraints, such as budget and return on investment (ROI) rate, are private types. We derive the truthfulness conditions with respect to private constraints for this multi-dimensional setting, and demonstrate any feasible allocation rule could be equivalently reduced to a series of non-decreasing functions on budget. However, the resulted allocation mapped from these non-decreasing functions generally follows an irregular shape, making it difficult to obtain a closed-form expression for the auction objective. To overcome this design difficulty, we propose a family of truthful automated bidding auction with personalized rank scores, similar to the Generalized Second-Price (GSP) auction. The intuition behind our design is to leverage personalized rank scores as the criteria to allocate items, and compute a critical ROI to transform the constraints on budget to the same dimension as ROI. The experimental results demonstrate that the proposed auction mechanism outperforms the widely used ad auctions, such as first-price auction and second-price auction, in various automated bidding environments.

翻译：自动出价是一种由机器学习驱动的新兴智能决策范式，已在在线广告领域得到广泛应用。在自动出价中，广告主评估长期多轮广告拍卖中的累积效用，并面临私人财务约束。基于这些独特特征，我们提出一种针对自动出价的广告拍卖新模型：广告主的估值是公开信息，而预算和投资回报率（ROI）等财务约束则为私人类型。我们推导了针对这种多维设定下私人约束的诚实性条件，并证明任何可行的分配规则均可等价转化为一系列关于预算的非递减函数。然而，由这些非递减函数映射得到的分配通常呈现不规则形状，导致拍卖目标难以获得闭式表达式。为解决这一设计难题，我们提出了一类采用个性化排名分数的诚实自动出价拍卖方案，类似于广义第二价格（GSP）拍卖。其设计核心是利用个性化排名分数作为物品分配准则，并计算关键ROI值，从而将预算约束转化为与ROI同维度的约束。实验结果表明，在多种自动出价环境中，所提出的拍卖机制优于广泛使用的一价拍卖和二价拍卖等广告竞拍方式。