  Online auctions are one of the most fundamental facets of the modern economy
and power an industry generating hundreds of billions of dollars a year in
revenue. Auction theory has historically focused on the question of designing
the best way to sell a single item to potential buyers, with the concurrent
objectives of maximizing revenue generated or welfare created. Theoretical
results in this area have typically relied on some prior Bayesian knowledge
agents were assumed to have on each-other. This assumption is no longer
satisfied in new markets such as online advertising: similar items are sold
repeatedly, and agents are unaware of each other or might try to manipulate
each-other. On the other hand, statistical learning theory now provides tools
to supplement those missing pieces of information given enough data, as agents
can learn from their environment to improve their strategies. This survey
covers recent advances in learning in repeated auctions, starting from the
traditional economic study of optimal one-shot auctions with a Bayesian prior.
We then focus on the question of learning optimal mechanisms from a dataset of
bidders' past values. The sample complexity as well as the computational
efficiency of different methods will be studied. We will also investigate
online variants where gathering data has a cost to be accounted for, either by
seller or buyers ("earning while learning"). Later in the survey, we will
further assume that bidders are also adaptive to the mechanism as they interact
repeatedly with the same seller. We will show how strategic agents can actually
manipulate repeated auctions, to their own advantage. All the questions
discussed in this survey are grounded in real-world applications and many of
the ideas and algorithms we describe are used every day to power the Internet
economy.
