We consider a causal inference problem frequently encountered in online advertising systems, where a publisher (e.g., Instagram, TikTok) interacts repeatedly with human users and advertisers by sporadically displaying to each user an advertisement selected through an auction. Each treatment corresponds to a parameter value of the advertising mechanism (e.g., auction reserve-price), and we want to estimate through experiments the corresponding long-term treatment effect (e.g., annual advertising revenue). In our setting, the treatment affects not only the instantaneous revenue from showing an ad, but also changes each user's interaction-trajectory, and each advertiser's bidding policy -- as the latter is constrained by a finite budget. In particular, each a treatment may even affect the size of the population, since users interact longer with a tolerable advertising mechanism. We drop the classical i.i.d. assumption and model the experiment measurements (e.g., advertising revenue) as a stopped random walk, and use a budget-splitting experimental design, the Anscombe Theorem, a Wald-like equation, and a Central Limit Theorem to construct confidence intervals for the long-term treatment effect.

翻译：本文研究在线广告系统中常见的因果推断问题，其中发布平台（如Instagram、TikTok）通过间歇性向用户展示拍卖选定的广告，与人类用户和广告商进行重复交互。每种处理对应广告机制的一个参数值（如拍卖保留价），我们希望通过实验估计相应的长期处理效应（如年度广告收入）。在我们的设定中，处理不仅影响展示广告的瞬时收益，还会改变每个用户的交互轨迹以及每个广告商的出价策略——因为后者的预算约束是有限的。特别地，由于用户对可容忍的广告机制交互时间更长，每种处理甚至可能影响总体规模。我们摒弃了经典的独立同分布假设，将实验测量值（如广告收入）建模为停止随机游走，并采用预算分割实验设计、Anscombe定理、Wald型方程以及中心极限定理来构建长期处理效应的置信区间。