On Non-Stationary Dynamic Pricing: Adaptivity and Optimality
2026-07-27 • Machine Learning
Machine Learning
AI summaryⓘ
The authors study how a company can set prices for products sold to customers over time when customer demand changes unpredictably. They assume demand depends on certain features and follows a model called a generalized linear model (GLM). To maximize revenue, the authors propose a new algorithm that detects changes quickly and adjusts pricing accordingly, achieving nearly the best possible performance without needing to know how often demand changes. They also prove that their method is theoretically optimal and show through experiments that it works well in practice. This advances the field by handling changing customer behavior better than previous approaches.
contextual dynamic pricingnon-stationaritygeneralized linear model (GLM)change-point detectionregret minimizationadaptive algorithmspiecewise stationaryminimax lower boundbandit problemsdesign-adjusted variation
Authors
Feiyu Jiang, Zifeng Zhao
Abstract
We study the contextual dynamic pricing problem under non-stationarity, where a firm sells products to $T$ sequentially arriving consumers that behave according to an unknown demand model that can change over time. The demand model is assumed to be a generalized linear model (GLM), allowing for a feature vector in $\mathbb{R}^d$ that encodes products and consumer information. To achieve optimal revenue (i.e., least regret), the firm needs to learn and exploit the unknown GLMs while monitoring for potential changes. We propose a multiscale change-point detection based algorithm that achieves a regret of order $\widetilde{O}(\sqrt{s_TdT}\wedge\{V_T^{1/3}d^{1/3}T^{2/3}+\sqrt{dT}\})$, where $s_T$ is the number of piecewise stationary segments and $V_T$ is a newly defined notion of design-adjusted variation budget of model parameters. Our algorithm is adaptive and does not require knowing $s_T$ or $V_T$. Moreover, to our knowledge, this is the first dynamic pricing algorithm that is adaptive to the nature of changes and achieves the best-of-both-worlds rate, thus closing a long-standing gap in the literature. We remark that, due to the varying contexts, existing works in the adaptive non-stationary bandit literature cannot be applied to achieve optimality for contextual dynamic pricing. The regret is further accompanied with a newly constructed minimax lower bound, confirming the optimality of our algorithm (up to logarithmic factors). Extensive numerical experiments are conducted to illustrate the efficiency and robustness of the proposed algorithm in non-stationary dynamic pricing.