🤖 AI Summary
This work addresses the challenges of traditional Bayesian optimization, which suffers from cubic computational complexity and difficulties in adapting global surrogate models to local optimization needs. The authors propose a novel approach that, for the first time, integrates recursive binary space partitioning into the Bayesian optimization framework. By jointly adapting Gaussian process modeling and acquisition strategies, the method achieves an adaptive balance between exploration and exploitation. This design reduces computational complexity from cubic to linear while maintaining high optimization performance. Empirical evaluations on seven standard benchmark functions spanning 6 to 124 dimensions demonstrate that the proposed method consistently outperforms state-of-the-art Bayesian optimization libraries, achieving superior efficiency and solution quality.
📝 Abstract
Bayesian optimization is a sequential method for minimizing objective functions that are expensive to evaluate and about which few assumptions can be made. By using all gathered data to train a Gaussian process model for the function and adaptively employing a mixture of global exploration and local exploitation, this method has been used for optimization in many fields including machine learning, automotive engineering and reinforcement learning. However, the standard method suffers from two problems: 1) with cubic computational complexity in the training-set size it eventually becomes computationally infeasible to train the model, and 2) globally modeling the objective function is not necessarily optimal given the local nature of minimization. Using flexible and recursive binary partitioning of the search space, we adapt both the modeling and acquisitive aspects of standard Bayesian optimization to work harmoniously with the partitioning scheme, thereby ameliorating both standard shortcomings. We compare our method against a commonly used Bayesian optimization library on seven challenging test functions, ranging in dimensionality from $6$ to $124$, and show that our method achieves superior optimization performance in all tests. In addition our method has linear computational complexity.