Contextual Pricing with Heterogeneous Buyers

We initiate the study of contextual dynamic pricing with a heterogeneous population of buyers, where a seller repeatedly (over $T$ rounds) posts prices 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 $\tilde{O}(K_{\star}\sqrt{dT})$, 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 $K_{\star}$.