In addition to maximizing the total revenue, decision-makers in lots of industries would like to guarantee balanced consumption across different resources. For instance, in the retailing industry, ensuring a balanced consumption of resources from different suppliers enhances fairness and helps main a healthy channel relationship; in the cloud computing industry, resource-consumption balance helps increase customer satisfaction and reduce operational costs. Motivated by these practical needs, this paper studies the price-based network revenue management (NRM) problem with both demand learning and fair resource-consumption balancing. We introduce the regularized revenue, i.e., the total revenue with a balancing regularization, as our objective to incorporate fair resource-consumption balancing into the revenue maximization goal. We propose a primal-dual-type online policy with the Upper-Confidence-Bound (UCB) demand learning method to maximize the regularized revenue. We adopt several innovative techniques to make our algorithm a unified and computationally efficient framework for the continuous price set and a wide class of balancing regularizers. Our algorithm achieves a worst-case regret of $\widetilde O(N^{5/2}\sqrt{T})$, where $N$ denotes the number of products and $T$ denotes the number of time periods. Numerical experiments in a few NRM examples demonstrate the effectiveness of our algorithm in simultaneously achieving revenue maximization and fair resource-consumption balancing

翻译：除了最大化总收益外，许多行业的决策者还需确保不同资源的消耗平衡。例如，在零售业中，确保来自不同供应商的资源消耗平衡有助于增进公平性并维护健康的渠道关系；在云计算行业，资源消耗平衡有助于提升客户满意度并降低运营成本。受这些实际需求的驱动，本文研究了同时涉及需求学习与公平资源消耗平衡的基于价格的网络收益管理问题。我们将正则化收益（即包含平衡正则项的总收益）作为目标函数，以将公平资源消耗平衡融入收益最大化目标。我们提出了一种采用上置信界需求学习方法的原始-对偶型在线策略，以最大化正则化收益。我们采用多项创新技术，使我们的算法成为适用于连续价格集及广泛平衡正则化函数的统一且计算高效的框架。该算法实现了最坏情况下的遗憾界$\widetilde O(N^{5/2}\sqrt{T})$，其中$N$表示产品数量，$T$表示时间周期数。在若干网络收益管理实例上的数值实验证明了我们的算法能同时有效实现收益最大化与公平资源消耗平衡。