Real-time bidding (RTB) systems, which utilize auctions to allocate user impressions to competing advertisers, continue to enjoy success in digital advertising. Assessing the effectiveness of such advertising remains a challenge in research and practice. This paper proposes a new approach to perform causal inference on advertising bought through such mechanisms. Leveraging the economic structure of first- and second-price auctions, we first show that the effects of advertising are identified by the optimal bids. Hence, since these optimal bids are the only objects that need to be recovered, we introduce an adapted Thompson sampling (TS) algorithm to solve a multi-armed bandit problem that succeeds in recovering such bids and, consequently, the effects of advertising while minimizing the costs of experimentation. We derive a regret bound for our algorithm which is order optimal and use data from RTB auctions to show that it outperforms commonly used methods that estimate the effects of advertising.

翻译：实时竞价（RTB）系统通过拍卖将用户展示机会分配给竞争广告商，在数字广告领域持续取得成功。评估此类广告的效果仍是研究与实践中的挑战。本文提出了一种新方法，对通过此类机制购买的广告进行因果推断。利用第一价格和第二价格拍卖的经济结构，我们首先证明广告效果可由最优出价识别。因此，由于只需恢复这些最优出价，我们引入一种改进的汤普森采样（TS）算法，以求解多臂老虎机问题，成功恢复出价并进而估计广告效果，同时最小化实验成本。我们推导出该算法的遗憾界，该界限达到阶最优，并利用RTB拍卖数据证明其优于常用的广告效果估计方法。