Robust Sampling Budget Allocation Under Deep Uncertainty
Robust Sampling Budget Allocation Under Deep Uncertainty
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DOI：
10.1109/tsmc.2022.3144363
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发表时间：
2022-10
期刊：
影响因子：
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通讯作者：
Michael Perry;Jie Xu;Edward Huang;C.-H. Chen
中科院分区：
文献类型：
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作者：
Michael Perry;Jie Xu;Edward Huang;C.-H. Chen
介绍了一种最优分配抽样预算的新方法。抽样预算分配问题在各种情况下经常出现。例如，在复杂工程系统的设计中，考虑到这些系统的复杂性和对新技术的不完全信息，设计者经常面临关于系统性能的深层次不确定性。因此，设计师需要在有限的预算下尝试多种替代设计。本文提出了一种在存在与系统性能有关的深度不确定性的情况下分配抽样预算的最小极大遗憾方法。目标是在有限的抽样预算和不完全信息下，最大化选择具有最小-最大遗憾的设计的概率。为了有效地解决最小极大后悔问题，提出了一种近似方法，该方法提供了具有可量化不确定性的良好解。这种方法的本质是，除了第一级优化外，所有的多级优化都可以通过响应面来消除，这一方法具有普遍适用于任何多级优化的额外好处。通过对较高级别决策变量的多个值进行采样，在给定这些样本值的情况下求解下一个较低级别的优化，并将响应面校准为目标函数值，从而消除了所需的优化。反复这样做可以将多级优化的复杂性降低到标准优化。不管优化中的层数是多少，重复这个过程最终只剩下一个优化，它的目标函数可以在给定最高级别变量的情况下直接计算。通过两个抽样分配实例的数值实验，证明了稳健抽样预算分配相对于非稳健公式的优势和所提出的求解方法的有效性。
A novel methodology is introduced for optimally allocating a sampling budget. Sampling budget allocation problems arise frequently in various settings. For example, in the design of complex engineering systems, given both the complexity of these systems and the imperfect information on new technologies, designers often face deep uncertainty as to system performance. Consequently, designers need to sample multiple alternative designs under a limited budget. This article proposes a minimax regret approach to allocate the sampling budget in the presence of deep uncertainty pertaining to system performance. The objective is to maximize the probability of selecting the design with the minimum–maximum regret under a limited sampling budget and imperfect information. To effectively solve the minimax regret problem, an approximation methodology that provides good solutions with quantifiable uncertainty is developed. The essence of the methodology, which has the added benefit of being generally applicable to any multilevel optimization, is that all but the first level of multilevel optimization can be eliminated via a response surface. By sampling many values of a higher level decision’s variables, solving the next lower level optimization given those samples values, and calibrating a response surface to the objective function value eliminate one required optimization. Doing this repeatedly reduces the complexity of the multilevel optimization to a standard optimization. Regardless of the number of levels in the optimization, repeating this process ultimately leaves one with a single optimization whose objective function can be directly computed, given the highest level variables. Numerical experiments with two sampling allocation examples demonstrate both the benefit of the robust sampling budget allocation versus nonrobust formulations and the effectiveness of the proposed solution approach.