Technical note: Finite‐time regret analysis of Kiefer‐Wolfowitz stochastic approximation algorithm and nonparametric multi‐product dynamic pricing with unknown demand

We consider the problem of nonparametric multi‐product dynamic pricing with unknown demand and show that the problem may be formulated as an online model‐free stochastic program, which can be solved by the classical Kiefer‐Wolfowitz stochastic approximation (KWSA) algorithm. We prove that the expect...

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Bibliographic Details
Published in:Naval research logistics Vol. 67; no. 5; pp. 368 - 379
Main Authors: Hong, L. Jeff, Li, Chenghuai, Luo, Jun
Format: Journal Article
Language:English
Published: Hoboken, USA John Wiley & Sons, Inc 01.08.2020
Wiley Subscription Services, Inc
Subjects:
Algorithms
Approximation
Constants
dynamic pricing and learning
Kiefer‐Wolfowitz algorithm
Lower bounds
Market prices
Mathematical analysis
nonparametric pricing policy
Nonparametric statistics
Policies
Pricing
Pricing policies
revenue management
stochastic approximation
ISSN:0894-069X, 1520-6750
Online Access:Get full text
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Summary:We consider the problem of nonparametric multi‐product dynamic pricing with unknown demand and show that the problem may be formulated as an online model‐free stochastic program, which can be solved by the classical Kiefer‐Wolfowitz stochastic approximation (KWSA) algorithm. We prove that the expected cumulative regret of the KWSA algorithm is bounded above by κ1T+κ2 where κ1, κ2 are positive constants and T is the number of periods for any T = 1, 2, …. Therefore, the regret of the KWSA algorithm grows in the order of T, which achieves the lower bounds known for parametric dynamic pricing problems and shows that the nonparametric problems are not necessarily more difficult to solve than the parametric ones. Numerical experiments further demonstrate the effectiveness and efficiency of our proposed KW pricing policy by comparing with some pricing policies in the literature.
Bibliography:Funding information
Accepted by René Caldentey, revenue management and marketplace design.
National Natural Science Foundation of China, 71531010; 71722006; 71991473; The Hong Kong Research Grants Council, GRF 11504017
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ISSN:0894-069X
1520-6750
DOI:10.1002/nav.21902