Online learning in repeated auctions

TL;DR

This paper develops online learning strategies for repeated Vickrey auctions, enabling bidders to adapt their bids over time with provable regret bounds in both stochastic and adversarial settings.

Contribution

It introduces the first comprehensive set of bidding strategies for repeated auctions with bandit feedback, applicable to stochastic and adversarial models.

Findings

Logarithmic regret in stochastic models

Sublinear regret in adversarial models

Matching minimax lower bounds established

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 and we simply compare our performance against that of the best fixed bid in hindsight. We show that sublinear regret is also achievable in this case and prove matching minimax lower bounds. To our knowledge, this is the first complete set of strategies for bidders participating in auctions of this type.