Contextual Dynamic Pricing with Heterogeneous Buyers

TL;DR

This paper introduces a new approach to dynamic pricing with heterogeneous buyers, leveraging contextual information and Bayesian methods to achieve near-optimal regret bounds in a setting where buyer valuations are unknown and diverse.

Contribution

It develops a novel contextual pricing algorithm based on optimistic posterior sampling that handles heterogeneity and unknown valuation distributions, with tight regret guarantees.

Findings

Regret bound of O(K_rac{dT}{ ext{logarithmic factors}}) for the contextual setting.

A variance-aware zooming algorithm for non-contextual pricing with optimal dependence on K_.

Theoretical analysis confirming tightness of the regret bounds.

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 $K_{\star}$.