Fine-Grained Derivative-Free Simultaneous Optimistic Optimization with Local Gaussian Process

Derivative-free optimization has achieved remarkable success across a variety of applications where the explicit formulation of an objective function is inaccessible. Learning an accurate surrogate model from solutions and their function values is crucial for derivative-free optimization. Methods for constructing global surrogate models, such as Bayesian optimization (BO), encounter the challenge of high learning cost, which impairs optimization efficiency. Splitting the entire search domain into smaller regions, a series of domain partition methods are proposed, like simultaneous optimistic optimization (SOO). It has demonstrated notable effectiveness in derivative-free optimization but still has room for improvement due to its relatively coarse-grained partition strategy. To this end, this paper proposes a fine-grained simultaneous optimistic optimization (FGSOO) method with local Gaussian process. Specifically, FGSOO designs a fine-grained partition strategy to endow SOO with the capability of cross-height comparison, and utilizes local Gaussian process to make nodes' potential more representative, so as to reduce the required number of solutions for learning surrogate models. Compared with BO, FGSOO reduces the learning cost. Meanwhile, compared with SOO, FGSOO could avoid unnecessary partition. The experimental results on real-world tasks, such as trajectory optimization and molecule substructure optimization, verify that FGSOO surpasses the compared methods in improving efficiency while maintaining effectiveness.