利用人类专家经验提升不确定参数优化问题的性能保障
The Value of Human Expertise
- 基于人类对最优解不大的先验信念设计评估策略
- 若最坏情况性能可建模为凸规划，则人效价值等于极大极小间隙
- 适用于有领域知识但数据不足的优化场景，如商品组合与路径规划
在未知参数的优化问题中，决策者认为若参数已知时最优解的值不太可能很大，这种信念源于未被数据捕捉的人类领域知识与物理交互经验。本文提出一种评估策略，当该信念成立时可提供更紧的性能保证。主要结果表明：若计算策略最坏情况性能为凸规划，则人类专家的价值——即信念能带来的性能保障最大提升——等于一个极大极小问题的极小极大差距。我们在商品组合优化和最短路径问题中展示了该方法的应用。
原文摘要 · Abstract (English)
We consider optimization applications with unknown parameters where the decision maker believes that the optimal value of the nominal problem-the optimization problem they would have solved if the true parameters were known-is unlikely to be large. This belief derives from information that humans have that is not captured in datasets, obtained from domain knowledge and interacting with the physical world. We propose an approach to evaluating policies that provides tighter performance guarantees if the decision maker's belief happens to be correct. Our main result shows that if computing a policy's worst-case performance is a convex program, then the value of human expertise-the maximum improvement in performance guarantees that can be obtained from the belief about the nominal problem-is equal to the minimax gap of a max-min problem. We illustrate our developments in assortment optimization and shortest path problems.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。