  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Wald's test no longer valid.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.
