Learning to Bid Without Knowing your Value
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We address online learning in complex auction settings, such as sponsored search auctions, where the value of the bidder is unknown to her, evolving in an arbitrary manner and observed only if the bidder wins an allocation. We leverage the structure of the utility of the bidder to provide algorithms with regret rates against the best fixed bid in hindsight, that are exponentially faster in convergence in terms of dependence on the action space, than what would have been derived by applying a generic bandit algorithm. Our results are enabled by analyzing a new online learning setting with outcome-based feedback, which generalizes learning with feedback graphs. We provide an online learning algorithm for this setting, of independent interest, with regret that grows only logarithmically with the number of actions and linearly only in the number of potential outcomes (the latter being very small in most auction settings).
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