Dynamic Pricing in the Linear Valuation Model using Shape Constraints

TL;DR

This paper introduces a shape-constrained, tuning-parameter free dynamic pricing method for the linear valuation model, leveraging isotonic regression under weaker assumptions, and demonstrates superior empirical performance.

Contribution

It presents a novel shape-constrained approach using isotonic regression for dynamic pricing, eliminating the need for tuning parameters and accommodating weaker assumptions on market noise.

Findings

Achieves lower empirical regret than existing methods.

Operates without tuning parameters.

Works under weaker assumptions on market noise.

Abstract

We propose a shape-constrained approach to dynamic pricing for censored data in the linear valuation model eliminating the need for tuning parameters commonly required by existing methods. Previous works have addressed the challenge of unknown market noise distribution $F_0$ using strategies ranging from kernel methods to reinforcement learning algorithms, such as bandit techniques and upper confidence bounds (UCB), under the assumption that $F_0$ satisfies Lipschitz (or stronger) conditions. In contrast, our method relies on isotonic regression under the weaker assumption that $F_0$ is $\alpha$-H\"older continuous for some $\alpha \in (0,1]$, for which we derive a regret upper bound. Simulations and experiments with real-world data obtained by Welltower Inc (a major healthcare Real Estate Investment Trust) consistently demonstrate that our method attains lower empirical regret in comparison to several existing methods in the literature while offering the advantage of being tuning-parameter free.