Contextual Dynamic Pricing with Heterogeneous Buyers

2025-12-10

AI Summary

This paper studies contextual dynamic pricing under buyer heterogeneity and unknown valuation distributions with finite support: over $T$ rounds, a seller sets prices based on $d$-dimensional context vectors and observes only binary purchase feedback. We introduce the first formal model capturing non-homogeneous buyer types and propose an Optimistic Posterior Sampling algorithm, achieving a tight regret bound of $ ilde{O}(K^star sqrt{dT})$, which is optimal in $d$ and $T$ (up to logarithmic factors). Furthermore, we design a variance-aware scaling technique that attains optimal dependence on $K^star$ in the non-contextual special case. Our theoretical analysis integrates Bayesian updating, contextual linear demand modeling, and adaptive zooming partitioning. This work establishes the first provably optimal learning framework for online contextual pricing in heterogeneous markets.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Online Learning & Bandits
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Advertising auctions, pricing, markets, and exchanges
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising

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 $K_{star}$.

Problem

• Develops contextual dynamic pricing algorithm for heterogeneous buyer valuation types.
• Achieves near-optimal regret bounds in dimensions and time for pricing.
• Refines non-contextual pricing with variance-aware algorithm for optimal dependence.

Innovation

• Optimistic posterior sampling for contextual pricing
• Variance-aware zooming algorithm for non-contextual case
• Regret bound tight in dimensions and time