Joint Value Estimation and Bidding in Repeated First-Price Auctions
This work addresses a practical challenge in online advertising by enabling efficient bidding without requiring the overlap condition from causal inference, though it is incremental in extending auction theory to specific outcome models.
The paper tackles the problem of regret minimization in repeated first-price auctions where bidders only observe win/loss outcomes, proposing algorithms for joint value estimation and bidding that achieve near-optimal regret bounds across adversarial, linear potential outcome, and linear treatment effect models.
We study regret minimization in repeated first-price auctions (FPAs), where a bidder observes only the realized outcome after each auction -- win or loss. This setup reflects practical scenarios in online display advertising where the actual value of an impression depends on the difference between two potential outcomes, such as clicks or conversion rates, when the auction is won versus lost. We analyze three outcome models: (1) adversarial outcomes without features, (2) linear potential outcomes with features, and (3) linear treatment effects in features. For each setting, we propose algorithms that jointly estimate private values and optimize bidding strategies, achieving near-optimal regret bounds. Notably, our framework enjoys a unique feature that the treatments are also actively chosen, and hence eliminates the need for the overlap condition commonly required in causal inference.