Online learning in repeated auctions

Motivated by online advertising auctions, we consider repeated Vickrey\nauctions where goods of unknown value are sold sequentially and bidders only\nlearn (potentially noisy) information about a good's value once it is\npurchased. We adopt an online learning approach with bandit feedback to model\nthis problem and derive bidding strategies for two models: stochastic and\nadversarial. In the stochastic model, the observed values of the goods are\nrandom variables centered around the true value of the good. In this case,\nlogarithmic regret is achievable when competing against well behaved\nadversaries. In the adversarial model, the goods need not be identical and we\nsimply compare our performance against that of the best fixed bid in hindsight.\nWe show that sublinear regret is also achievable in this case and prove\nmatching minimax lower bounds. To our knowledge, this is the first complete set\nof strategies for bidders participating in auctions of this type.\n

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