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In “Optimal No-Regret Learning in Repeated First-Price Auctions,” Y. Han, W. Tsachy, and Z. Zhou study online learning in repeated first-price auctions where a bidder, only observing the winning bid at the end of each auction, learns to adaptively bid to maximize her cumulative payoff. To achieve this goal, the bidder faces censored feedback: If she wins the bid, then she is not able to observe the highest bid of the other bidders, which we assume is i.i.d. drawn from an unknown distribution. In this paper, they develop the first learning algorithm that achieves a near-optimal regret bound, by exploiting two structural properties of first-price auctions, that is, the specific feedback structure and payoff function.
Han et al. (Mon,) studied this question.