On Non-Stationary Dynamic Pricing: Adaptivity and Optimality

2026-07-27

AI Summary

This work addresses the problem of dynamic pricing under non-stationary environments, where consumer demand follows an unknown time-varying generalized linear model. The paper proposes the first adaptive algorithm that requires no prior knowledge of either the number of change points or the magnitude of changes. By integrating multi-scale change-point detection with online learning, the method uniformly handles both abrupt and gradual shifts, achieving near-optimal revenue without assuming knowledge of the underlying piecewise-stationary structure. Theoretical analysis establishes a regret bound of $\widetilde{O}(\sqrt{s_T d T} \wedge (V_T^{1/3} d^{1/3} T^{2/3} + \sqrt{d T}))$, which matches a newly derived minimax lower bound, thereby closing a significant theoretical gap in the literature. Empirical experiments further demonstrate the algorithm’s efficiency and robustness.

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.

Problem

• non-stationary dynamic pricing
• contextual dynamic pricing
• generalized linear model
• change-point detection
• regret minimization

Innovation

• non-stationary dynamic pricing
• contextual bandits
• change-point detection
• adaptive regret
• generalized linear model