Learning to Bid Without Knowing your Value
This addresses the challenge for bidders in sponsored search auctions to optimize bids without knowing their value, representing a strong specific gain in auction theory.
The paper tackles the problem of online learning in complex auctions where a bidder's value is unknown and evolving, by developing an algorithm that achieves regret rates exponentially faster in convergence than generic bandit methods, with experimental results showing robust performance.
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 and the partial feedback that bidders typically receive in auctions, in order 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 and almost equivalent to what would have been achieved in the full information setting. 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). Last but not least, we show that our algorithm outperforms the bandit approach experimentally and that this performance is robust to dropping some of our theoretical assumptions or introducing noise in the feedback that the bidder receives.