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。

潜在能量驱动之旅：通过在能量基潜空间中扩展探索的黑盒优化

Latent Energy-Based Odyssey: Black-Box Optimization via Expanded  Exploration in the Energy-Based Latent Space

The goal of offline black-box optimization (BBO) is to optimize an expensive
black-box function using a fixed dataset of function evaluations. Prior works
consider forward approaches that learn surrogates to the black-box function and
inverse approaches that directly map function values to corresponding points in
the input domain of the black-box function. These approaches are limited by the
quality of the offline dataset and the difficulty in learning one-to-many
mappings in high dimensions, respectively. We propose Denoising Diffusion
Optimization Models (DDOM), a new inverse approach for offline black-box
optimization based on diffusion models. Given an offline dataset, DDOM learns a
conditional generative model over the domain of the black-box function
conditioned on the function values. We investigate several design choices in
DDOM, such as re-weighting the dataset to focus on high function values and the
use of classifier-free guidance at test-time to enable generalization to
function values that can even exceed the dataset maxima. Empirically, we
conduct experiments on the Design-Bench benchmark and show that DDOM achieves
results competitive with state-of-the-art baselines.

该论文介绍了一种新的离线黑盒优化的逆向方法 ——DDOM，基于扩散模型，它能够通过学习条件生成模型来进行优化，其在 Design-Bench 基准测试中的表现与最先进的基线相媲美。