Several fundamental problems in science and engineering consist of global optimization tasks involving unknown high-dimensional (black-box) functions that map a set of controllable variables to the outcomes of an expensive experiment. Bayesian Optimization (BO) techniques are known to be effective in tackling global optimization problems using a relatively small number objective function evaluations, but their performance suffers when dealing with high-dimensional outputs. To overcome the major challenge of dimensionality, here we propose a deep learning framework for BO and sequential decision making based on bootstrapped ensembles of neural architectures with randomized priors. Using appropriate architecture choices, we show that the proposed framework can approximate functional relationships between design variables and quantities of interest, even in cases where the latter take values in high-dimensional vector spaces or even infinite-dimensional function spaces. In the context of BO, we augmented the proposed probabilistic surrogates with re-parameterized Monte Carlo approximations of multiple-point (parallel) acquisition functions, as well as methodological extensions for accommodating black-box constraints and multi-fidelity information sources. We test the proposed framework against state-of-the-art methods for BO and demonstrate superior performance across several challenging tasks with high-dimensional outputs, including a constrained optimization task involving shape optimization of rotor blades in turbo-machinery.
翻译:科学和工程方面的几个根本问题包括:全球优化任务,涉及未知的高维(黑盒)功能,绘制一套可控变量,以绘制昂贵实验结果的一组可控变量。据了解,巴伊西亚优化(BO)技术能够有效地利用数量相对较少的客观功能评价解决全球优化问题,但其性能在处理高维产出时会受到影响。为了克服维度这一重大挑战,我们在此提议一个深入的BO学习框架,以及基于螺旋形团团团团的神经结构以及随机前置信息源的顺序决策。我们通过适当的结构选择,表明拟议的框架可以大致显示设计变量和兴趣数量之间的功能关系,即使后者在高维矢量空间甚至无限功能空间中取值,也能有效解决全球优化问题。在BO范围内,我们用重新配置的多点(平行)获取功能的蒙特卡洛近似值来补充拟议的概率性超常代孕药,以及用于容纳黑盒制约和多种纤维化信息来源的方法扩展。我们测试拟议的框架,以高维值的系统优化方式,包括高维级任务,在BO和高端优化过程中展示高压式任务。