Contextual Dynamic Pricing with Heterogeneous Buyers
This work addresses pricing optimization for sellers in online markets with diverse buyer types, representing a novel extension beyond homogeneous assumptions.
The paper tackles the problem of contextual dynamic pricing with heterogeneous buyers, where a seller sets prices based on observable contexts and receives binary feedback, and it develops an algorithm achieving a regret bound of ̃O(K_{★}√dT), which is proven tight in d and T up to logarithmic terms.
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 $K_{\star}$.