Derivative-free tree optimization for complex systems
Ye Wei Bo Peng Ruiwen Xie Yangtao Chen Yu Qin Peng Wen Stefan Bauer Po-Yen Tung
A tremendous range of design tasks in materials, physics, and biology can be
formulated as finding the optimum of an objective function depending on many
parameters without knowing its closed-form expression or the derivative.
Traditional derivative-free optimization techniques often rely on strong
assumptions about objective functions, thereby failing at optimizing non-convex
systems beyond 100 dimensions. Here, we present a tree search method for
derivative-free optimization that enables accelerated optimal design of
high-dimensional complex systems. Specifically, we introduce stochastic tree
expansion, dynamic upper confidence bound, and short-range backpropagation
mechanism to evade local optimum, iteratively approximating the global optimum
using machine learning models. This development effectively confronts the
dimensionally challenging problems, achieving convergence to global optima
across various benchmark functions up to 2,000 dimensions, surpassing the
existing methods by 10- to 20-fold. Our method demonstrates wide applicability
to a wide range of real-world complex systems spanning materials, physics, and
biology, considerably outperforming state-of-the-art algorithms. This enables
efficient autonomous knowledge discovery and facilitates self-driving virtual
laboratories. Although we focus on problems within the realm of natural
science, the advancements in optimization techniques achieved herein are
applicable to a broader spectrum of challenges across all quantitative
disciplines.