Budget pacing is a popular service that has been offered by major internet advertising platforms since their inception. Budget pacing systems seek to optimize advertiser returns subject to budget constraints through smooth spending of advertiser budgets. In the past few years, autobidding products that provide real-time bidding as a service to advertisers have seen a prominent rise in adoption. A popular autobidding stategy is value maximization subject to return-on-spend (ROS) constraints. For historical or business reasons, the algorithms that govern these two services, namely budget pacing and RoS pacing, are not necessarily always a single unified and coordinated entity that optimizes a global objective subject to both constraints. The purpose of this work is to study the benefits of coordinating budget and RoS pacing services from an empirical and theoretical perspective. We compare (a) a sequential algorithm that first constructs the advertiser's ROS-pacing bid and then lowers that bid for budget pacing, with (b) the optimal joint algorithm that optimizes advertiser returns subject to both budget and ROS constraints. We establish the superiority of joint optimization both theoretically as well as empirically based on data from a large advertising platform. In the process, we identify a third algorithm with minimal interaction between services that retains the theoretical properties of the joint optimization algorithm and performs almost as well empirically as the joint optimization algorithm. This algorithm eases the transition from a sequential to a fully joint implementation by minimizing the amount of interaction between the two services.

翻译：预算节奏是一项主流互联网广告平台自成立以来便提供的服务。预算节奏系统通过平滑分配广告主预算，在预算约束下优化广告主收益。近年来，为广告主提供实时竞价服务的自动竞价产品普及率显著提升。一种流行的自动竞价策略是在投入回报率（ROS）约束下实现价值最大化。由于历史或业务原因，管理这两项服务（即预算节奏与ROS节奏）的算法未必始终是统一协调的实体，以同时优化满足双重约束的全局目标。本研究旨在从实证与理论角度探讨协调预算与ROS节奏服务的优势。我们比较了（a）先构建广告主ROS节奏出价、再为预算节奏下调该出价的顺序算法，与（b）在预算与ROS双重约束下优化广告主收益的最优联合算法。通过理论推导及基于大型广告平台数据的实证分析，我们证明了联合优化的优越性。在此过程中，我们识别出第三种算法——该算法最小化服务间的交互，既保留了联合优化算法的理论特性，又在实证中达到与联合优化算法近乎相同的性能。该算法通过减少两项服务间的交互量，降低了从顺序实现向完全联合实现的过渡难度。