  With the advent and increasing consolidation of e-commerce, digital
advertising has very recently replaced traditional advertising as the main
marketing force in the economy. In the past four years, a particularly
important development in the digital advertising industry is the shift from
second-price auctions to first-price auctions for online display ads. This
shift immediately motivated the intellectually challenging question of how to
bid in first-price auctions, because unlike in second-price auctions, bidding
one's private value truthfully is no longer optimal. Following a series of
recent works in this area, we consider a differentiated setup: we do not make
any assumption about other bidders' maximum bid (i.e. it can be adversarial
over time), and instead assume that we have access to a hint that serves as a
prediction of other bidders' maximum bid, where the prediction is learned
through some blackbox machine learning model. We consider two types of hints:
one where a single point-prediction is available, and the other where a hint
interval (representing a type of confidence region into which others' maximum
bid falls) is available. We establish minimax optimal regret bounds for both
cases and highlight the quantitatively different behavior between the two
settings. We also provide improved regret bounds when the others' maximum bid
exhibits the further structure of sparsity. Finally, we complement the
theoretical results with demonstrations using real bidding data.
