论文标题
贝叶斯正交正常优化概率阈值鲁棒性测量
Bayesian Quadrature Optimization for Probability Threshold Robustness Measure
论文作者
论文摘要
在许多产品开发问题中，产品的性能受两种称为设计参数和环境参数的参数。虽然前者是完全可控的，但后者因使用产品的环境而异。这种问题的挑战是找到最大化产品性能达到所需必要水平的设计参数，鉴于环境参数的变化。在本文中，我们将这个实际问题作为主动学习（AL）问题提出，并提出了具有理论上保证的性能的有效算法。我们的基本思想是将高斯工艺（GP）模型用作产品开发过程的替代模型，然后将我们的问题作为贝叶斯正交正常优化问题，以实现概率阈值鲁棒性（PTR）度量。我们得出了PTR度量的可靠间隔，并提出了对PTR度量的优化和水平设置估计的AL算法。我们阐明了所提出的算法的理论特性，并证明了它们在合成和现实产品开发问题中的效率。
In many product development problems, the performance of the product is governed by two types of parameters called design parameter and environmental parameter. While the former is fully controllable, the latter varies depending on the environment in which the product is used. The challenge of such a problem is to find the design parameter that maximizes the probability that the performance of the product will meet the desired requisite level given the variation of the environmental parameter. In this paper, we formulate this practical problem as active learning (AL) problems and propose efficient algorithms with theoretically guaranteed performance. Our basic idea is to use Gaussian Process (GP) model as the surrogate model of the product development process, and then to formulate our AL problems as Bayesian Quadrature Optimization problems for probabilistic threshold robustness (PTR) measure. We derive credible intervals for the PTR measure and propose AL algorithms for the optimization and level set estimation of the PTR measure. We clarify the theoretical properties of the proposed algorithms and demonstrate their efficiency in both synthetic and real-world product development problems.
