Context-Based Dynamic Pricing with Separable Demand Models
Jinzhi Bu, David Simchi-Levi, Chonghuan Wang
Management Science · 2026 · Volume 72 · Issue 8
Abstract
Motivated by the empirical evidence observed from the real-world data set, this paper studies context-based dynamic pricing with separable demand models. Consider a seller selling a product over a finite horizon of T periods and facing an unknown expected demand function that admits a separable structure 𝑓 ( 𝑝 ) + 𝑔 ( 𝒙 ) f ( p ) + g ( x ) , where 𝑝 ∈ ℝ p ∈ R and 𝒙 ∈ ℝ 𝑑 x ∈ R d denote the product’s price and features, respectively. The seller does not know the exact expression of 𝑓 ( 𝑝 ) f ( p ) or 𝑔 ( 𝒙 ) g ( x ) but can dynamically adjust prices in each period based on the observed features and demands to learn their forms. The seller’s objective is to maximize the T -period expected revenue. We systematically characterize the statistical complexity of the online learning problem under three configurations of demand models with different structures of 𝑓 ( 𝑝 ) f ( p ) and 𝑔 ( 𝒙 ) g ( x ) . For each model, we design an efficient online learning algorithm with a provable regret upper bound. We also show that the upper bound is generally unimprovable by proving a matching regret lower bound in certain parameter regimes. Our results reveal fundamental differences in the optimal regret rates when 𝑓 ( 𝑝 ) f ( p ) and 𝑔 ( 𝒙 ) g ( x ) are endowed with different structures. The numerical results demonstrate that our learning algorithms are more effective than benchmark algorithms for all the three models and also show the effects of the parameters associated with 𝑓 ( 𝑝 ) f ( p ) and 𝑔 ( 𝒙 ) g ( x ) on the algorithm’s empirical regret. This paper was accepted by J. George Shanthikumar, data science. Funding: The authors acknowledge support from the MIT Data Science Laboratory. J. Bu acknowledges support from the Research Grants Council of Hong Kong [Early Career Scheme Grant PolyU 25505322]. Supplemental Material: The online appendices and data files are available at https://doi.org/10.1287/mnsc.2022.02260 .
Keywords
separable model, dynamic pricing, contextual information, online learning
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