基于数量的网络收益管理的近优原始对偶法
Near-Optimal Primal-Dual Algorithms for Quantity-Based Network Revenue Management
摘要：
我们研究了基于数量的网络收益管理（NRM）问题，决策者必须合理地接受或拒绝每个到达的客户请求，目标是最大限度地提高总收入给定的有限资源。由于众所周知的维数灾难，通过动态规划对问题的精确解在计算上是难以处理的。现有文献中的工作利用确定性线性规划（DLP）的解来设计渐近最优算法。这些算法依赖于反复求解DLP来实现接近最优的遗憾界限。然而，实时重复计算DLP解决方案是耗时的，特别是在可能涉及数亿需求单元的大规模问题中。在本文中，我们提出了创新的算法NRM问题，易于实现，不需要解决任何DLP。我们的算法实现了$O(\log k)$的遗憾界，其中$k$是系统的大小。据我们所知，这是第一个NRM算法，（i）有一个$o(\sqrt{k})$渐近遗憾界，（ii）不需要解决任何DLP。
英文摘要：
We study the canonical quantity-based network revenue management (NRM) problem where the decision-maker must irrevocably accept or reject each arriving customer request with the goal of maximizing the total revenue given limited resources. The exact solution to the problem by dynamic programming is computationally intractable due to the well-known curse of dimensionality. Existing works in the literature make use of the solution to the deterministic linear program (DLP) to design asymptotically optimal algorithms. Those algorithms rely on repeatedly solving DLPs to achieve near-optimal regret bounds. It is, however, time-consuming to repeatedly compute the DLP solutions in real time, especially in large-scale problems that may involve hundreds of millions of demand units. In this paper, we propose innovative algorithms for the NRM problem that are easy to implement and do not require solving any DLPs. Our algorithm achieves a regret bound of $O(\log k)$, where $k$ is the system size. To the best of our knowledge, this is the first NRM algorithm that (i) has an $o(\sqrt{k})$ asymptotic regret bound, and (ii) does not require solving any DLPs.
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。
