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With the advent and increasing consolidation of e-commerce, digitaladvertising has very recently replaced traditional advertising as the mainmarketing force in the economy. In the past four years, a particularlyimportant development in the digital advertising industry is the shift fromsecond-price auctions to first-price auctions for online display ads. Thisshift immediately motivated the intellectually challenging question of how tobid in first-price auctions, because unlike in second-price auctions, biddingone's private value truthfully is no longer optimal. Following a series ofrecent works in this area, we consider a differentiated setup: we do not makeany assumption about other bidders' maximum bid (i.e. it can be adversarialover time), and instead assume that we have access to a hint that serves as aprediction of other bidders' maximum bid, where the prediction is learnedthrough some blackbox machine learning model. We consider two types of hints:one where a single point-prediction is available, and the other where a hintinterval (representing a type of confidence region into which others' maximumbid falls) is available. We establish minimax optimal regret bounds for bothcases and highlight the quantitatively different behavior between the twosettings. We also provide improved regret bounds when the others' maximum bidexhibits the further structure of sparsity. Finally, we complement thetheoretical results with demonstrations using real bidding data.

Leveraging the Hints: Adaptive Bidding in Repeated First-Price Auctions