发表机构
University of Warwick（沃里克大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究参数不确定性下随机优化中顺序数据收集的最优停止问题，提出收益驱动停止框架，在此基础上开发停止策略，经报童问题实验验证，该策略能减少不必要数据收集并实现近最优决策性能。
AI 中文摘要
数据驱动的优化通常需要在解决潜在决策问题之前收集数据以估计不确定的模型参数。然而在实践中，数据采集可能产生不可忽视的成本，因此确定何时停止额外数据收集至关重要。本文研究了参数不确定性下随机优化中顺序数据收集的最优停止问题。我们提出了一个平衡信息增益和采样成本的收益驱动停止框架。在贝叶斯学习框架内对未知分布参数建模，并随着新观测值的收集顺序更新信念。在每次迭代中，决策者评估相对于单位采样成本的额外数据的预期边际收益，并决定是继续采样还是停止并实施优化决策。基于此框架，我们开发了几种停止策略。通过具有指数分布需求的报童问题对所提出的策略进行评估。数值实验将这些策略与固定预算和事后基准策略进行比较。结果表明，收益驱动的停止规则可以在实现接近最优决策性能的同时，大幅减少不必要的数据收集，证明了自适应停止在数据驱动优化中的有效性。
英文摘要
Data-driven optimization often requires collecting data to estimate uncertain model parameters before solving the underlying decision problem. In practice, however, data acquisition may incur non-negligible costs, making it critical to determine when to stop additional data collection. In this paper, we study an optimal stopping problem for sequential data collection in stochastic optimization under parameter uncertainty. We propose a benefit-driven stopping framework that balances information gain and sampling cost. We model the unknown distribution parameter within a Bayesian learning framework and update beliefs sequentially as new observations are collected. At each iteration, the decision maker evaluates the expected marginal benefit of additional data relative to the unit sampling cost and determines whether to continue sampling or stop and implement the optimization decision. Based on this framework, we develop several stopping policies. The proposed policies are evaluated through a newsvendor problem with exponentially distributed demand. Numerical experiments compare the policies with fixed-budget and hindsight benchmark strategies. The results show that benefit-driven stopping rules can substantially reduce unnecessary data collection while achieving near-optimal decision performance, demonstrating the effectiveness of adaptive stopping in data-driven optimization.
