A Distributionally Robust Approach to Black-Box Optimization
A Distributionally Robust Approach to Black-Box Optimization
复制标题
一种分布式稳健的黑盒优化方法
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
K. Willcox
中科院分区：
文献类型：
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作者：
A. Philpott;Michael G. Kapteyn;K. Willcox
决定如何表示和管理不确定性是设计复杂系统的重要组成部分。广泛使用的是一种概率方法——给每个不确定变量分配一个概率分布。然而，这给设计师提出了假设或估计这些概率分布的任务；不可避免地容易出错的任务。本文通过提出一个分布式稳健设计优化问题来解决这一挑战，并提出了求解该问题的计算效率高的算法。在分布鲁棒优化（DRO）方法中，设计者承认他们无法精确地指定不确定变量的概率分布，而是指定所谓的可能分布的模糊集。本文以一个喇叭设计问题为例，探讨了在不确定条件下，从数据估计概率分布时产生的误差如何影响传统的多目标优化设计的实现性能。研究发现，在降低风险目标上给予一定的重视，会使设计对这些误差具有更强的鲁棒性，从而在真实分布下实现更好的平均性能，而不是仅仅将所有的研究重点放在平均性能的优化上。相比之下，DRO方法能够发现在给定相同数据时使用多目标方法无法实现的设计。在某些情况下，这些DRO设计明显优于使用多目标方法的设计。
Deciding how to represent and manage uncertainty is a vital part of designing complex systems. Widely used is a probabilistic approach—assigning a probability distribution to each uncertain variable. However, this presents the designer with the task of assuming or estimating these probability distributions from data; a task which is inevitably prone to error. This paper addresses this challenge by formulating a distributionally robust design optimization problem, and presents computationally e � cient algorithms for solving the problem. In distributionally robust optimization (DRO) methods, the designer acknowl-edges that they are unable to exactly specify a probability distribution for the uncertain variables, and instead specifies a so-called ambiguity set of possible distributions. This paper uses an acoustic horn design problem to explore how the error incurred in estimating a probability distribution from data a ↵ ects the realized performance of designs found using a traditional multi-objective optimization under uncertainty. It is found that placing some importance on a risk reduction objective results in designs that are more robust to these errors, and thus have a better mean performance realized under the true distribution than if the designer were to focus all e ↵ orts on optimizing for mean performance alone. In contrast, the DRO approach is able to uncover designs that are not attainable using the multi-objective approach when given the same data. These DRO designs in some cases significantly outperform those designs found using the multi-objective approach.