A Distributionally Robust Approach to Black-Box Optimization
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 distri...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
American Institute of Aeronautics and Astronautics
2018
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| Online Access: | http://hdl.handle.net/1721.1/116646 https://orcid.org/0000-0003-2156-9338 |
| Summary: | 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 ecient
algorithms for solving the problem. In distributionally robust optimization (DRO) methods, the designer acknowledges 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. |
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