Offline Black-Box Optimization (BBO) aims at optimizing a black-box function
using the knowledge from a pre-collected offline dataset of function values and
corresponding input designs. However, the high-dimensional and
highly-multimodal input design space of black-box function pose inherent
challenges for most existing methods that model and operate directly upon input
designs. These issues include but are not limited to high sample complexity,
which relates to inaccurate approximation of black-box function; and
insufficient coverage and exploration of input design modes, which leads to
suboptimal proposal of new input designs. In this work, we consider finding a
latent space that serves as a compressed yet accurate representation of the
design-value joint space, enabling effective latent exploration of high-value
input design modes. To this end, we formulate an learnable energy-based latent
space, and propose Noise-intensified Telescoping density-Ratio Estimation
(NTRE) scheme for variational learning of an accurate latent space model
without costly Markov Chain Monte Carlo. The optimization process is then
exploration of high-value designs guided by the learned energy-based model in
the latent space, formulated as gradient-based sampling from a
latent-variable-parameterized inverse model. We show that our particular
parameterization encourages expanded exploration around high-value design
modes, motivated by inversion thinking of a fundamental result of conditional
covariance matrix typically used for variance reduction. We observe that our
method, backed by an accurately learned informative latent space and an
expanding-exploration model design, yields significant improvements over strong
previous methods on both synthetic and real world datasets such as the
design-bench suite.

离线黑盒优化目标是通过预先采集的函数值和相关输入设计的离线数据集的知识来优化黑盒函数。我们提出了一种可学习的能量驱动潜空间模型，以及一种基于噪声增强的望远镜密度比估计方案，用于变分学习准确的潜空间模型。通过所学的能量驱动模型在潜空间中的梯度导向采样，我们展示了该方法在高价值设计模式的探索中取得了显著改进。