未知需求曲线与服务分布队列的在线学习与优化
Online Learning and Optimization for Queues with Unknown Demand Curve and Service Distribution
AI总结：
针对排队系统服务费与容量优化问题，提出在线学习框架，自动纳入参数估计误差，无需单独参数估计步骤，通过理论收敛性与遗憾分析及仿真验证其优于传统PTO方法。
摘要：
我们研究排队系统中的优化问题，其中服务提供商选择最优服务费p和服务能力μ，以最大化累积期望利润（服务收入减去容量成本和延迟惩罚）。传统的“先预测后优化”（PTO）方法分两步：首先从数据中估计模型参数（如到达率和服务时间分布），然后基于估计参数优化模型。PTO的主要缺点是其解的精度往往对参数估计误差高度敏感，因为PTO无法将这些误差（步骤1）与优化解的质量（步骤2）正确关联。为解决此问题，我们开发了一种在线学习框架，在解的处方过程中自动纳入上述参数估计误差；这是一种集成方法，能够“学习”最优解，而无需像PTO那样将参数估计设为单独步骤。我们通过（i）包括算法收敛性和遗憾（算法学习最优策略随时间需支付的“代价”）分析的理论结果，以及（ii）通过对多种代表性示例的仿真实验进行工程验证，证实了在线学习方法的有效性。我们还对PTO和在线学习方法进行了仔细比较。
英文摘要：
We investigate an optimization problem in a queueing system where the service provider selects the optimal service fee p and service capacity μto maximize the cumulative expected profit (the service revenue minus the capacity cost and delay penalty). The conventional predict-then-optimize (PTO) approach takes two steps: first, it estimates the model parameters (e.g., arrival rate and service-time distribution) from data; second, it optimizes a model based on the estimated parameters. A major drawback of PTO is that its solution accuracy can often be highly sensitive to the parameter estimation errors because PTO is unable to properly link these errors (step 1) to the quality of the optimized solutions (step 2). To remedy this issue, we develop an online learning framework that automatically incorporates the aforementioned parameter estimation errors in the solution prescription process; it is an integrated method that can "learn" the optimal solution without needing to set up the parameter estimation as a separate step as in PTO. Effectiveness of our online learning approach is substantiated by (i) theoretical results including the algorithm convergence and analysis of the regret ("cost" to pay over time for the algorithm to learn the optimal policy), and (ii) engineering confirmation via simulation experiments of a variety of representative examples. We also provide careful comparisons for PTO and the online learning method.
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。
