Joint Feedback Loop for Spend and Return-On-Spend Constraints

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.