Policy Optimization Using Semiparametric Models for Dynamic Pricing

by   Jianqing Fan, et al.

In this paper, we study the contextual dynamic pricing problem where the market value of a product is linear in its observed features plus some market noise. Products are sold one at a time, and only a binary response indicating success or failure of a sale is observed. Our model setting is similar to Javanmard and Nazerzadeh [2019] except that we expand the demand curve to a semiparametric model and need to learn dynamically both parametric and nonparametric components. We propose a dynamic statistical learning and decision-making policy that combines semiparametric estimation from a generalized linear model with an unknown link and online decision-making to minimize regret (maximize revenue). Under mild conditions, we show that for a market noise c.d.f. F(·) with m-th order derivative (m≥ 2), our policy achieves a regret upper bound of Õ_d(T^2m+1/4m-1), where T is time horizon and Õ_d is the order that hides logarithmic terms and the dimensionality of feature d. The upper bound is further reduced to Õ_d(√(T)) if F is super smooth whose Fourier transform decays exponentially. In terms of dependence on the horizon T, these upper bounds are close to Ω(√(T)), the lower bound where F belongs to a parametric class. We further generalize these results to the case with dynamically dependent product features under the strong mixing condition.


page 1

page 2

page 3

page 4


Distribution-free Contextual Dynamic Pricing

Contextual dynamic pricing aims to set personalized prices based on sequ...

On Dynamic Pricing with Covariates

We consider the dynamic pricing problem with covariates under a generali...

Perishability of Data: Dynamic Pricing under Varying-Coefficient Models

We consider a firm that sells a large number of products to its customer...

Dynamic Pricing with Finitely Many Unknown Valuations

Motivated by posted price auctions where buyers are grouped in an unknow...

Dynamic Pricing and Learning under the Bass Model

We consider a novel formulation of the dynamic pricing and demand learni...

Towards Agnostic Feature-based Dynamic Pricing: Linear Policies vs Linear Valuation with Unknown Noise

In feature-based dynamic pricing, a seller sets appropriate prices for a...

Incentive-aware Contextual Pricing with Non-parametric Market Noise

We consider a dynamic pricing problem for repeated contextual second-pri...

Please sign up or login with your details

Forgot password? Click here to reset