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 $K_{\star}$.

翻译：本文首次研究了面向异质买家群体的上下文动态定价问题：卖方在$T$轮重复交易中，根据可观测的$d$维上下文信息发布价格，并接收二元购买反馈。与先前假设买家类型同质的研究不同，本设定中买家的估值类型从具有有限支撑集大小$K_{\star}$的未知分布中抽取。我们提出了一种基于乐观后验采样的上下文定价算法，其遗憾上界为$\widetilde{O}(K_{\star}\sqrt{dT})$，并证明该上界在$d$和$T$维度上除对数项外是紧致的。最后，针对非上下文定价场景，我们改进了分析方法，提出一种方差感知的缩放算法，实现了对$K_{\star}$的最优依赖关系。