Context-Based Dynamic Pricing with Separable Demand Models

Abstract

Motivated by the empirical evidence observed from the real-world dataset, 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 $f(p)+g(x)$, where $p\in\mathbb{R}$ and $x\in\mathbb{R}^d$ denote the product's price and features respectively. The seller does not know the exact expression of $f(p)$ or $g(x)$, 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 $f(p)$ and $g(x)$. 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 $f(p)$ and $g(x)$ 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 $f(p)$ and $g(x)$ on the algorithm's empirical regret.

Keywords: Separable Demand, Dynamic Pricing, Contextual Information, Online Learning