Demand Balancing in Primal-Dual Optimization for Blind Network Revenue Management

TL;DR

This paper introduces a new primal-dual algorithm for network revenue management with unknown demand, achieving improved regret bounds and practical efficiency through a demand balancing technique.

Contribution

It presents a novel demand balancing method within a primal-dual framework, improving regret bounds and practicality over previous algorithms for nonparametric demand.

Findings

Achieves a regret of  O(N^{3.25}     T)

Outperforms benchmark algorithms in numerical experiments

Provides a practical and theoretically optimal solution for nonparametric demand management

Abstract

This paper proposes a practically efficient algorithm with optimal theoretical regret which solves the classical network revenue management (NRM) problem with unknown, nonparametric demand. Over a time horizon of length $T$, in each time period the retailer needs to decide prices of $N$ types of products which are produced based on $M$ types of resources with unreplenishable initial inventory. When demand is nonparametric with some mild assumptions, Miao and Wang (2021) is the first paper which proposes an algorithm with $O(\text{poly}(N,M,\ln(T))\sqrt{T})$ type of regret (in particular, $\tilde O(N^{3.5}\sqrt{T})$ plus additional high-order terms that are $o(\sqrt{T})$ with sufficiently large $T\gg N$). In this paper, we improve the previous result by proposing a primal-dual optimization algorithm which is not only more practical, but also with an improved regret of $\tilde O(N^{3.25}\sqrt{T})$ free from additional high-order terms. A key technical contribution of the proposed algorithm is the so-called demand balancing, which pairs the primal solution (i.e., the price) in each time period with another price to offset the violation of complementary slackness on resource inventory constraints. Numerical experiments compared with several benchmark algorithms further illustrate the effectiveness of our algorithm.