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.

翻译：离线黑盒优化旨在利用预先收集的函数值及其对应输入设计构成的离线数据集知识来优化黑盒函数。然而，黑盒函数的高维且高度多模态的输入设计空间对大多数直接在输入设计上建模和操作的方法构成了固有挑战。这些问题包括但不限于：高样本复杂度（与黑盒函数近似不准确相关），以及输入设计模态覆盖不足和探索不充分（导致新输入设计方案次优）。本研究致力于寻找一个能作为设计-值联合空间压缩且精确表示的潜在空间，从而实现对高价值输入设计模态的有效潜在探索。为此，我们构建了一个可学习的能量基潜在空间，并提出噪声增强型伸缩密度比估计方案，用于变分学习精确的潜在空间模型而无需昂贵的马尔可夫链蒙特卡洛方法。优化过程随后转化为在潜在空间中基于习得的能量模型引导的高价值设计探索，其形式化表述为从潜在变量参数化逆模型进行梯度采样。我们证明了我们的特定参数化方式能促进围绕高价值设计模态的扩展探索，其动机源于对通常用于方差缩减的条件协方差矩阵基本结果的逆向思考。实验表明，凭借精确习得的信息化潜在空间和扩展探索模型设计，我们的方法在合成数据集和真实世界数据集（如design-bench套件）上均较以往强基线方法取得显著提升。