Before revision:  problem, we propose a modified Thompson Sampling (TS) algorithm that concurrently learns the optimal bidding policy and estimates the expected effect of displaying the ad while minimizing economic losses from potential sub-optimal bidding . Simulations show that not only the proposed method successfully accomplishes the advertiser's goals, but also does so at a much lower cost than more conventional experimentation policies aimed at performing causal inference.
After revision:  problem, we propose a modified Thompson Sampling (TS) algorithm that estimates causal effects of advertising while minimizing the costs of experimentation to the advertiser by simultaneously learning the optimal bidding policy and estimates the expected effect of displaying the ad while minimizing economic losses from potential sub-optimal bidding . Simulations show that not only the proposed method successfully accomplishes the advertiser's goals, but also does so at a much lower cost than more conventional experimentation policies aimed at performing causal inference.