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：科学与工程领域的若干基础问题涉及全局优化任务，其核心在于对未知高维（黑箱）函数进行优化——该函数将一组可控变量映射至昂贵实验的输出结果。贝叶斯优化技术虽能以较少目标函数评估次数有效处理全局优化问题，但在面对高维输出时性能会显著下降。为克服这一维度性核心挑战，本文提出基于随机先验引导的神经网络自助集成架构的深度学习框架，用于贝叶斯优化与序贯决策。通过合理架构选择，我们证明该框架能够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穷维函数空间。在贝叶斯优化语境中，我们采用重参数化蒙特卡洛近似多点（并行）采集函数对概率代理模型进行增强，并拓展方法论以兼容黑箱约束与多保真度信息源。我们将所提框架与当前最先进贝叶斯优化方法进行对比测试，结果表明该方法在多个高维输出挑战性任务中表现出卓越性能，其中包含透平机械转子叶片形状优化的约束优化任务。