Personalized Dynamic Pricing Based on Improved Thompson Sampling

Abstract

This study investigates personalized pricing with demand learning. We first encode consumer-personalized feature information into high-dimensional vectors, then establish the relationship between this feature vector and product demand using a logit model, and finally learn demand parameters through historical transaction data. To address the balance between learning and revenue, we introduce the Thompson Sampling algorithm. Considering the difficulty of Bayesian inference in Thompson Sampling owing to high-dimensional feature vectors, we improve the basic Thompson Sampling by approximating the likelihood function of the logit model with the Pólya-Gamma (PG) distribution and by proposing a Thompson Sampling algorithm based on the PG distribution. To validate the proposed algorithm’s effectiveness, we conduct experiments using both simulated data and real loan data provided by the Columbia University Revenue Management Center. The study results demonstrate that the Thompson Sampling algorithm based on the PG distribution proposed outperforms traditional Laplace approximation methods regarding convergence speed and regret value in both real and simulated data experiments. The real-time personalized pricing algorithm developed here not only enriches the theoretical research of personalized dynamic pricing, but also provides a theoretical basis and guidance for enterprises to implement personalized pricing.

Keywords

• personalized dynamic pricing
• demand learning
• Thompson sampling algorithm
• Bayesian inference
• Pólya-gamma distribution