The (Marginal) Value of a Search Ad: An Online Causal Framework for Repeated Second-price Auctions

Existing auto-bidding algorithms in digital advertising often treat the value of an ad opportunity as the revenue obtained when an ad is shown and/or clicked, and bid accordingly. This can lead to wasteful spending because the true value is the marginal gain from paid exposure: even without winning a sponsored slot, an advertiser may still earn revenue via an organic search result (e.g., on Google or Amazon). Motivated by recent work, we model ad value as a treatment effect—the outcome difference between winning and losing the auction—and study online learning for bidding in second-price (Vickrey) auctions under this causal perspective. We develop algorithms that attain rate-optimal regret under several feedback models. A key ingredient exploits the information revealed by the second-price payment rule, which strictly improves regret relative to analogous learning problems in first-price auctions.

Most current digital advertising exchanges adopt real-time bidding for ad opportunity allocations: the advertisers bid for every ad opportunity in real-time and the winner displays her ad and pays accordingly. For an advertiser to maximizer her revenue, it is important to develop proper bidding algorithms that automatically adapt to the estimated value of an ad opportunity (e.g. conversion rate) and the bidding environment (e.g. the competing bids). Existing literature often considers the ad value as the outcome/conversion after the advertiser wins and displays her ad. This overlooks the possible positive outcome when she does not display the ad, for example, from the organic results in a search. In this work, we complement the literature by considering the ad value as a causal outcome difference between displaying an ad and not. We focus on the second-price auctions which are widely used by the platforms for search ads. Our contributions include provably optimal algorithms under novel technical ingredients and numerical simulations with an easy-to-implement algorithm variant.