Causal Inference on Stopped Random Walks in Online Advertising

TL;DR

This paper develops a method for estimating long-term effects of advertising treatments in online platforms by modeling user interactions as stopped random walks, accounting for complex dependencies and non-i.i.d. data.

Contribution

It introduces a novel framework combining stopped random walk modeling with statistical inference techniques for causal effects in online advertising.

Findings

Provides confidence intervals for long-term treatment effects.

Models user interactions as stopped random walks.

Utilizes Anscombe Theorem and CLT for inference.

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.