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.

本文提出了一个深度学习框架，基于具有随机先验的 bootstrap 整合的神经体系结构，用于贝叶斯优化和连续决策。该框架能够在高维输出的情况下逼近设计变量和感兴趣数量之间的函数关系，测试表明该方法在优化轮毂叶片的形状等高度复杂的任务中具有明显的优越性。