Researchers constantly strive to explore larger and more complex search
spaces in various scientific studies and physical experiments. However, such
investigations often involve sophisticated simulators or time-consuming
experiments that make exploring and observing new design samples challenging.
Previous works that target such applications are typically sample-inefficient
and restricted to vector search spaces. To address these limitations, this work
proposes a constrained multi-objective optimization (MOO) framework, called
BREATHE, that searches not only traditional vector-based design spaces but also
graph-based design spaces to obtain best-performing graphs. It leverages
second-order gradients and actively trains a heteroscedastic surrogate model
for sample-efficient optimization. In a single-objective vector optimization
application, it leads to 64.1% higher performance than the next-best baseline,
random forest regression. In graph-based search, BREATHE outperforms the
next-best baseline, i.e., a graphical version of Gaussian-process-based
Bayesian optimization, with up to 64.9% higher performance. In a MOO task, it
achieves up to 21.9$\times$ higher hypervolume than the state-of-the-art
method, multi-objective Bayesian optimization (MOBOpt). BREATHE also
outperforms the baseline methods on most standard MOO benchmark applications.

为了解决传统方法在探索大型和复杂的搜索空间时的样本效率问题，本研究提出了一种称为 BREATHE 的受约束多目标优化框架，可以在向量和图形设计空间中搜索，以获得最佳性能的结果。通过利用二阶梯度和主动训练异方差代理模型，该方法在向量和图形优化应用中的性能均明显高于当前最佳基准方法，并在多目标优化任务中实现更高的超体积值。

BREATHE: 基于二阶梯度和异方差模拟的设计空间探索

BREATHE: Second-Order Gradients and Heteroscedastic Emulation based  Design Space Exploration

Bayesian optimization (BO) is a popular approach for sample-efficient
optimization of black-box objective functions. While BO has been successfully
applied to a wide range of scientific applications, traditional approaches to
single-objective BO only seek to find a single best solution. This can be a
significant limitation in situations where solutions may later turn out to be
intractable. For example, a designed molecule may turn out to violate
constraints that can only be reasonably evaluated after the optimization
process has concluded. To address this issue, we propose Rank-Ordered Bayesian
Optimization with Trust-regions (ROBOT) which aims to find a portfolio of
high-performing solutions that are diverse according to a user-specified
diversity metric. We evaluate ROBOT on several real-world applications and show
that it can discover large sets of high-performing diverse solutions while
requiring few additional function evaluations compared to finding a single best
solution.

ROBOT 使用排序和信任区间的方法来找到不同的高性能解决方案，相较于寻找单一最佳解决方案，只需要进行少量的额外函数评估。