Contextual Dynamic Pricing with Heterogeneous Buyers
Thodoris Lykouris, Sloan Nietert, Princewill Okoroafor, Chara Podimata, Julian Zimmert
TL;DR
This paper advances contextual dynamic pricing for heterogenous buyers by modeling buyer types as draws from an unknown distribution with finite support K★. It introduces an optimistic posterior sampling (OPS) framework, plus a perturbation-based extension (POPS) to handle infinite model classes, and establishes a near-optimal regret of $\tilde{O}(K★\sqrt{dT})$, with a matching lower bound $\Omega(\sqrt{K★ d T})$. A non-contextual refinement (ZoomV) achieves $\tilde{O}(\min\{\sqrt{K★T}, T^{2/3}\})$ via variance-aware zooming, while stronger ex-post type observability yields even tighter bounds $\tilde{O}(\sqrt{\min\{K★,d\}T})$. The work highlights how heterogeneity and feedback richness shape the difficulty of pricing under online learning, and it lays groundwork for scalable algorithms in practical settings with multiple buyer types and contextual information.
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 $K_{\star}$.