Dynamic Incentive-Aware Learning: Robust Pricing in Contextual Auctions

Motivated by pricing in ad exchange markets, we consider the problem of robust learning of reserve prices against strategic buyers in repeated contextual second-price auctions. Buyers' valuations \new{for} an item depend on the context that describes the item. However, the seller is not aware of the relationship between the context and buyers' valuations, i.e., buyers' preferences. The seller's goal is to design a learning policy to set reserve prices via observing the past sales data, and her objective is to minimize her regret for revenue, where the regret is computed against a clairvoyant policy that knows buyers' heterogeneous preferences. Given the seller's goal, utility-maximizing buyers have the incentive to bid untruthfully in order to manipulate the seller's learning policy. We propose two learning policies that are robust to such strategic behavior. These policies use the outcomes of the auctions, rather than the submitted bids, to estimate the preferences while controlling the long-term effect of the outcome of each auction on the future reserve prices. The first policy called Contextual Robust Pricing (CORP) is designed for the setting where the market noise distribution is known to the seller and achieves a T-period regret of $O(d\log(Td) \log (T))$, where $d$ is the dimension of {the} contextual information. The second policy, which is a variant of the first policy, is called Stable CORP (SCORP). This policy is tailored to the setting where the market noise distribution is unknown to the seller and belongs to an ambiguity set. We show that the SCORP policy has a T-period regret of $O(\sqrt{d\log(Td)}\;T^{2/3})$.