Advertisers that engage in real-time bidding (RTB) to display their ads commonly have two goals: learning their optimal bidding policy and estimating the expected effect of exposing users to their ads. Typical strategies to accomplish one of these goals tend to ignore the other, creating an apparent tension between the two. This paper exploits the economic structure of the bid optimization problem faced by advertisers to show that these two objectives can actually be perfectly aligned. By framing the advertiser’s problem as a multi-armed bandit (MAB) 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.