Feiyu Jiang

Fan Wang, Feiyu Jiang, Zifeng Zhao et al.

Dynamic pricing strategies are crucial for firms to maximize revenue by adjusting prices based on market conditions and customer characteristics. However, designing optimal pricing strategies becomes challenging when historical data are limited, as is often the case when launching new products or entering new markets. One promising approach to overcome this limitation is to leverage information from related products or markets to inform the focal pricing decisions. In this paper, we explore transfer learning for nonparametric contextual dynamic pricing under a covariate shift model, where the marginal distributions of covariates differ between source and target domains while the reward functions remain the same. We propose a novel Transfer Learning for Dynamic Pricing (TLDP) algorithm that can effectively leverage pre-collected data from a source domain to enhance pricing decisions in the target domain. The regret upper bound of TLDP is established under a simple Lipschitz condition on the reward function. To establish the optimality of TLDP, we further derive a matching minimax lower bound, which includes the target-only scenario as a special case and is presented for the first time in the literature. Extensive numerical experiments validate our approach, demonstrating its superiority over existing methods and highlighting its practical utility in real-world applications.

Zifeng Zhao, Feiyu Jiang, Yi Yu

We study contextual dynamic pricing problems where a firm sells products to $T$ sequentially-arriving consumers, behaving according to an unknown demand model. The firm aims to minimize its regret over a clairvoyant that knows the model in advance. The demand follows a generalized linear model (GLM), allowing for stochastic feature vectors in $\mathbb R^d$ encoding product and consumer information. We first show the optimal regret is of order $\sqrt{dT}$, up to logarithmic factors, improving existing upper bounds by a $\sqrt{d}$ factor. This optimal rate is materialized by two algorithms: a confidence bound-type algorithm and an explore-then-commit (ETC) algorithm. A key insight is an intrinsic connection between dynamic pricing and contextual multi-armed bandit problems with many arms with a careful discretization. We further study contextual dynamic pricing under local differential privacy (LDP) constraints. We propose a stochastic gradient descent-based ETC algorithm achieving regret upper bounds of order $d\sqrt{T}/ε$, up to logarithmic factors, where $ε>0$ is the privacy parameter. The upper bounds with and without LDP constraints are matched by newly constructed minimax lower bounds, characterizing costs of privacy. Moreover, we extend our study to dynamic pricing under mixed privacy constraints, improving the privacy-utility tradeoff by leveraging public data. This is the first time such setting is studied in the dynamic pricing literature and our theoretical results seamlessly bridge dynamic pricing with and without LDP. Extensive numerical experiments and real data applications are conducted to illustrate the efficiency and practical value of our algorithms.