发表机构
University College London; Purdue University（伦敦大学学院; 普渡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对拥塞依赖加入的动态服务推荐问题，提出两种近似算法（拟多项式时间近似方案和LP引导算法），分别实现近最优和(1-1/e)近似保证，并证明单调性是问题可处理的关键边界。
AI 中文摘要
现代服务平台通常在客户决定是否使用服务之前，向其提供实时拥塞信息，例如预期等待时间。这产生了服务推荐中的跨期权衡：将客户引导至某项服务可能产生即时价值，但由此产生的拥塞可能使该服务对未来客户的吸引力降低。我们通过一个有限时域随机优化问题来研究这种权衡，在该问题中，平台在多个服务之间进行动态推荐，每个服务由一个队列表示，客户的加入概率随拥塞程度而降低。我们首先将该问题表述为马尔可夫决策过程，并表明最优决策通常依赖于联合拥塞状态，从而导致状态空间过大。我们开发了两种互补的近似算法来克服这一维数灾难。首先，我们提供了一种拟多项式时间近似方案，该方案通过对模型原始参数进行截断和舍入来压缩联合拥塞状态，同时仔细考虑这些近似如何影响系统的随机演化，以建立近最优性。其次，我们开发了一种多项式时间的LP引导算法，该算法用服务级别的边际信息替代联合状态表示，并在更一般的服务和加入动态下实现(1-1/e)近似保证。最后，我们表明单调加入行为（即随着服务变得更加拥塞，客户加入的可能性降低）标志着基本的可处理性边界：如果没有单调性，该问题在任意常数因子内近似都是NP难的。这确立了单调性作为关键的行为属性，使得在拥塞依赖加入引入的复杂性下，可处理的动态服务推荐成为可能。
英文摘要
Modern service platforms often provide customers with real-time congestion information, such as anticipated waiting times, before they decide whether to use a service. This creates an intertemporal tradeoff in service recommendation: directing a customer to a service may generate immediate value, but the resulting congestion can make that service less attractive to future customers. We study this tradeoff through a finite-horizon stochastic optimization problem in which a platform dynamically recommends among multiple services, each represented by a queue, with customers' joining probabilities decreasing with congestion. We first formulate the problem as a Markov decision process and show that optimal decisions generally depend on the joint congestion state, giving rise to a prohibitively large state space. We develop two complementary approximation algorithms that overcome this curse of dimensionality. First, we provide a quasi-polynomial-time approximation scheme that uses truncation and rounding of the model primitives to compress the joint congestion state, while carefully accounting for how these approximations affect the stochastic evolution of the system to establish near-optimality. Second, we develop a polynomial-time LP-guided algorithm that replaces the joint-state representation with service-level marginal information and achieves a (1-1/e) approximation guarantee under substantially more general service and joining dynamics. Finally, we show that monotone joining behavior, whereby customers become less likely to join as a service becomes more congested, marks a fundamental tractability boundary: without monotonicity, the problem is NP-hard to approximate within any constant factor. This establishes monotonicity as a key behavioral property that enables tractable dynamic service recommendation despite the complexity introduced by congestion-dependent joining.
