Causal Inference on Stopped Random Walks in Online Advertising
- URL: http://arxiv.org/abs/2602.05997v1
- Date: Thu, 05 Feb 2026 18:43:29 GMT
- Title: Causal Inference on Stopped Random Walks in Online Advertising
- Authors: Jia Yuan Yu,
- Abstract summary: We consider a causal inference problem in online advertising systems.<n>Each treatment corresponds to a parameter value of the advertising mechanism.<n>We estimate through experiments the corresponding long-term treatment effect.
- Score: 2.758187691493102
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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.
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