We study a two-sided market, wherein, price-sensitive heterogeneous customers and servers arrive and join their respective queues. A compatible customer-server pair can then be matched by the platform, at which point, they leave the system. Our objective is to design pricing and matching algorithms that maximize the platform's profit, while maintaining reasonable queue lengths. As the demand and supply curves governing the price-dependent arrival rates may not be known in practice, we design a novel online-learning-based pricing policy and establish its near-optimality. In particular, we prove a tradeoff among three performance metrics: $\tilde{O}(T^{1-\gamma})$ regret, $\tilde{O}(T^{\gamma/2})$ average queue length, and $\tilde{O}(T^{\gamma})$ maximum queue length for $\gamma \in (0, 1/6]$, significantly improving over existing results [1]. Moreover, barring the permissible range of $\gamma$, we show that this trade-off between regret and average queue length is optimal up to logarithmic factors under a class of policies, matching the optimal one as in [2] which assumes the demand and supply curves to be known. Our proposed policy has two noteworthy features: a dynamic component that optimizes the tradeoff between low regret and small queue lengths; and a probabilistic component that resolves the tension between obtaining useful samples for fast learning and maintaining small queue lengths.

翻译：我们研究一个双边市场，其中价格敏感的异质客户和服务器到达并加入各自的队列。平台随后可以匹配兼容的客户-服务器对，匹配完成后双方离开系统。我们的目标是设计定价与匹配算法，在维持合理队列长度的同时最大化平台利润。由于控制价格依赖到达率的需求与供给曲线在实践中可能未知，我们设计了一种新颖的基于在线学习的定价策略，并证明其近最优性。具体而言，我们证明了三个性能指标之间的权衡关系：对于$\gamma \in (0, 1/6]$，获得$\tilde{O}(T^{1-\gamma})$遗憾、$\tilde{O}(T^{\gamma/2})$平均队列长度和$\tilde{O}(T^{\gamma})$最大队列长度，这显著改进了现有结果[1]。此外，在允许的$\gamma$范围之外，我们证明该遗憾与平均队列长度的权衡在某一策略类下达到对数因子内的最优性，与已知需求供给曲线情形下的最优结果[2]相匹配。我们提出的策略具有两个显著特征：动态优化低遗憾与小队列长度之间权衡的动态组件；以及解决快速学习所需有效样本获取与小队列长度维持之间矛盾的随机化组件。