Nonparametric Distributional Black-Box Optimization via Diffusion Process

Abstract

Sampling-based black-box optimization, e.g., zeroth-order optimization and Evolution strategy, is important for the material design, molecular design and etc. However, existing sampling-based black-box optimization methods only employ simple parametric distribution, typically Gaussian distribution, as the sampling distribution to generate queries. This limits the capabilities of modeling complex distribution to generate good candidates and influence the query efficiency. In this work, we propose a novel nonparametric black-box optimization method that performs proximal distributional update for sampling. Particularly, we derive the closed-form update rule based on the diffusion process (e.g., Ornstein–Uhlenbeck process). Our sampling and updating method supports black-box target function $f(\cdot)$ without accessing the $\nabla f$, which is critical for our nonparametric distributional black-box optimization.