## Bisection-Based Pricing for Repeated Contextual Auctions against Strategic Buyer

### Anton Zhiyanov · Alexey Drutsa

Keywords: [ Game Theory and Mechanism Design ] [ Online Learning / Bandits ] [ Online Learning, Active Learning, and Bandits ]

Abstract: We are interested in learning algorithms that optimize revenue in repeated contextual posted-price auctions where a single seller faces a single strategic buyer. In our setting, the buyer maximizes his expected cumulative discounted surplus, and his valuation of a good is assumed to be a fixed function of a $d$-dimensional context (feature) vector. We introduce a novel deterministic learning algorithm that is based on ideas of the Bisection method and has strategic regret upper bound of $O(\log^2 T)$. Unlike previous works, our algorithm does not require any assumption on the distribution of context information, and the regret guarantee holds for any realization of feature vectors (adversarial upper bound). To construct our algorithm we non-trivially adopted techniques of integral geometry to act against buyer strategicness and improved the penalization trick to work in contextual auctions.