Online learning in repeated auctions

Jonathan Weed, Vianney Perchet, Philippe Rigollet

Research output: Contribution to journalConference article

Abstract

Motivated by online advertising auctions, we consider repeated Vickrey auctions where goods of unknown value are sold sequentially and bidders only learn (potentially noisy) information about a good's value once it is purchased. We adopt an online learning approach with bandit feedback to model this problem and derive bidding strategies for two models: stochastic and adversarial. In the stochastic model, the observed values of the goods are random variables centered around the true value of the good. In this case, logarithmic regret is achievable when competing against well behaved adversaries. In the adversarial model, the goods need not be identical. Comparing our performance against that of the best fixed bid in hindsight, we show that sublinear regret is also achievable in this case. For both the stochastic and adversarial models, we prove matching minimax lower bounds showing our strategies to be optimal up to lower-order terms. To our knowledge, this is the first complete set of strategies for bidders participating in auctions of this type.

Original languageEnglish (US)
Pages (from-to)1562-1583
Number of pages22
JournalJournal of Machine Learning Research
Volume49
Issue numberJune
StatePublished - Jun 6 2016
Event29th Conference on Learning Theory, COLT 2016 - New York, United States
Duration: Jun 23 2016Jun 26 2016

Keywords

  • Bandit problems
  • Repeated auctions
  • Second price auctions
  • Vickrey auctions

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence

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  • Cite this

    Weed, J., Perchet, V., & Rigollet, P. (2016). Online learning in repeated auctions. Journal of Machine Learning Research, 49(June), 1562-1583.