Contextual Dynamic Pricing with Heterogeneous Buyers

Thodoris Lykouris, Sloan Nietert, Princewill Okoroafor, Chara Podimata, Julian Zimmert

Keywords: dynamic pricing, bandits, contextual

TL;DR: contextual dynamic pricing with heterogenous buyers using optimistic posterior sampling

Abstract: We initiate the study of contextual dynamic pricing with a heterogeneous population of buyers, where a seller repeatedly posts prices (over $T$ rounds) that depend on the observable $d$-dimensional context and receives binary purchase feedback. Unlike prior work assuming homogeneous buyer types, in our setting the buyer's valuation type is drawn from an unknown distribution with finite support size $K_{\star}$. We develop a contextual pricing algorithm based on optimistic posterior sampling with regret $\widetilde{O}(K_{\star}\sqrt{dT})$, which we prove to be tight in $d$ and $T$ up to logarithmic terms. Finally, we refine our analysis for the non-contextual pricing case, proposing a variance-aware zooming algorithm that achieves the optimal dependence on $K_{\star}$.

Primary Area: Theory (e.g., control theory, learning theory, algorithmic game theory)

Submission Number: 22846