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Motivated by pricing in ad exchange markets, we consider the problem ofrobust learning of reserve prices against strategic buyers in repeatedcontextual second-price auctions. Buyers' valuations for an item depend on thecontext that describes the item. However, the seller is not aware of therelationship between the context and buyers' valuations, i.e., buyers'preferences. The seller's goal is to design a learning policy to set reserveprices via observing the past sales data, and her objective is to minimize herregret for revenue, where the regret is computed against a clairvoyant policythat knows buyers' heterogeneous preferences. Given the seller's goal,utility-maximizing buyers have the incentive to bid untruthfully in order tomanipulate the seller's learning policy. We propose learning policies that arerobust to such strategic behavior. These policies use the outcomes of theauctions, rather than the submitted bids, to estimate the preferences whilecontrolling the long-term effect of the outcome of each auction on the futurereserve prices. When the market noise distribution is known to the seller, wepropose a policy called Contextual Robust Pricing (CORP) that achieves aT-period regret of $O(d\log(Td) \log (T))$, where $d$ is the dimension of {the}contextual information. When the market noise distribution is unknown to theseller, we propose two policies whose regrets are sublinear in $T$.

Dynamic Incentive-aware Learning: Robust Pricing in Contextual Auctions