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 multi-fidelity optimization task involving shape optimization of rotor blades in turbo-machinery.

翻译：科学与工程中的若干基础问题涉及全局优化任务，需要将一组可控变量映射到昂贵实验结果的未知高维（黑箱）函数。贝叶斯优化技术以较少的代价函数评估次数在处理全局优化问题中表现卓越，但其在高维输出场景下的性能显著受限。为克服维度灾难这一核心挑战，本文提出一种基于随机先验引导的神经网络自助聚合架构的深度学习框架，用于贝叶斯优化与序贯决策。通过合理的架构选择，我们证明该框架能够有效逼近设计变量与目标量之间的函数关系，即便后者取值于高维向量空间甚至无限维函数空间。在贝叶斯优化场景中，我们采用重参数化蒙特卡洛近似方法将多点（并行）采集函数与所提出的概率代理模型相结合，同时扩展了处理黑箱约束与多保真信息源的方法论框架。我们将所提框架与当前最优贝叶斯优化方法进行对比测试，结果表明其在多项涉及高维输出的挑战性任务中均表现出更优性能，包括涡轮机械转子叶片形状优化的约束多保真优化任务。