Uncertainty Quantification for Demand Prediction in Contextual Dynamic Pricing

TL;DR

This paper develops a debiased method to construct accurate confidence intervals for demand functions in dynamic pricing, addressing bias issues from sequential data collection and providing asymptotic guarantees.

Contribution

It introduces a novel debiased estimator for demand prediction in dynamic pricing, enabling valid confidence intervals despite distributional bias from sequential data.

Findings

Debiased estimator achieves asymptotic normality.

Provides point-wise and uniform confidence intervals.

Addresses bias in demand function estimation from sequential data.

Abstract

Data-driven sequential decision has found a wide range of applications in modern operations management, such as dynamic pricing, inventory control, and assortment optimization. Most existing research on data-driven sequential decision focuses on designing an online policy to maximize the revenue. However, the research on uncertainty quantification on the underlying true model function (e.g., demand function), a critical problem for practitioners, has not been well explored. In this paper, using the problem of demand function prediction in dynamic pricing as the motivating example, we study the problem of constructing accurate confidence intervals for the demand function. The main challenge is that sequentially collected data leads to significant distributional bias in the maximum likelihood estimator or the empirical risk minimization estimate, making classical statistics approaches such as the Wald's test no longer valid. We address this challenge by developing a debiased approach and provide the asymptotic normality guarantee of the debiased estimator. Based this the debiased estimator, we provide both point-wise and uniform confidence intervals of the demand function.