盲网络收益管理中原始-对偶优化的需求平衡
Demand Balancing in Primal-Dual Optimization for Blind Network Revenue Management
AI总结：
本文针对需求未知的非参数网络收益管理问题，提出一种基于需求平衡的原始-对偶优化算法，将遗憾界从 $\tilde O(N^{3.5}\sqrt{T})$ 改进为 $\tilde O(N^{3.25}\sqrt{T})$ 并消除高阶项，同时具有更强的实用性。
摘要：
本文提出了一种具有最优理论遗憾的实用高效算法，用于解决需求未知且非参数化的经典网络收益管理（NRM）问题。在长度为 $T$ 的时间范围内，零售商需要在每个时间段决定 $N$ 种产品的价格，这些产品基于 $M$ 种初始库存不可补充的资源进行生产。当需求为非参数且满足一些温和假设时，Miao 和 Wang（2021）首次提出了一个遗憾为 $O(\text{poly}(N,M,\ln(T))\sqrt{T})$ 类型的算法（具体为 $\tilde O(N^{3.5}\sqrt{T})$ 加上额外的高阶项，当 $T\gg N$ 足够大时这些高阶项为 $o(\sqrt{T})$）。本文通过提出一种原始-对偶优化算法改进了先前的结果，该算法不仅更实用，而且具有改进的遗憾界 $\tilde O(N^{3.25}\sqrt{T})$，且不含额外的高阶项。所提算法的一个关键技术贡献是所谓的需求平衡，它在每个时间段将原始解（即价格）与另一个价格配对，以抵消资源库存约束上互补松弛条件的违反。与多个基准算法对比的数值实验进一步说明了我们算法的有效性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
