Parameter-Adaptive Dynamic Pricing

TL;DR

This work tackles dynamic pricing under unknown demand-function parameters by eliminating dependence on the Hölder exponent $\beta$ and Lipschitz constant $L$. It introduces PADP, a discretization-based linear-bandit approach that uses local polynomial regression and layered data partitioning to adapt to unknown parameters. Theoretical results show minimax-type regret bounds and an extension to linear contextual effects (CDP-LDP), with adaptive estimation of the smoothness parameter. Empirical results demonstrate PADP's superior performance over prior non-adaptive methods, highlighting its practical impact for real-world pricing under parameter uncertainty.

Abstract

Dynamic pricing is crucial in sectors like e-commerce and transportation, balancing exploration of demand patterns and exploitation of pricing strategies. Existing methods often require precise knowledge of the demand function, e.g., the H{ö}lder smoothness level and Lipschitz constant, limiting practical utility. This paper introduces an adaptive approach to address these challenges without prior parameter knowledge. By partitioning the demand function's domain and employing a linear bandit structure, we develop an algorithm that manages regret efficiently, enhancing flexibility and practicality. Our Parameter-Adaptive Dynamic Pricing (PADP) algorithm outperforms existing methods, offering improved regret bounds and extensions for contextual information. Numerical experiments validate our approach, demonstrating its superiority in handling unknown demand parameters.

Figures (2)

• Figure 1: Relative regret curve with Hölder smooth demand.
• Figure 2: Relative regret curve with the very smooth demand.

Theorems & Definitions (26)

• Proposition 3.1
• Lemma 3.1
• Lemma 3.2
• Lemma 3.3
• Lemma 3.4
• Theorem 3.1
• Lemma 4.1
• Theorem 4.1
• Definition 4.1
• Lemma 4.2