Funneled Bayesian Optimization for Design, Tuning and Control of Autonomous Systems

Area of Science:

• Robotics and Autonomous Systems
• Machine Learning
• Optimization

Background:

• Robotics and autonomous systems face challenges in algorithm tuning, control, and design, often requiring solutions to global optimization problems with expensive evaluations.
• Bayesian optimization (BO) is crucial for sample-efficient global optimization, utilizing probabilistic surrogate models like Gaussian processes (GPs).
• Standard GPs assume stationary functions, which may not capture complex real-world dynamics.

Purpose of the Study:

• To develop a novel kernel function for Bayesian optimization that accommodates nonstationary behavior in surrogate models.
• To improve the performance of Bayesian optimization in applications with expensive evaluations and complex underlying functions.
• To enhance both local exploitation and global exploration capabilities within the Bayesian optimization framework.

Main Methods:

• Introduction of a novel kernel function designed for Bayesian optimization, enabling adaptive local nonstationary behavior.
• Development of a surrogate model capable of reconstructing nonstationarity despite irregular sampling inherent in BO.
• Extensive experimental validation across diverse benchmarks including machine learning hyperparameter tuning, reinforcement learning, control problems, and UAV wing optimization.

Main Results:

• The proposed kernel effectively reconstructs nonstationary functions even with irregular sampling distributions.
• The novel kernel demonstrates improved local search (exploitation) without compromising global search (exploration).
• The method outperforms state-of-the-art Bayesian optimization techniques on both stationary and nonstationary problems.

Conclusions:

• The new kernel function offers a significant advancement for Bayesian optimization, particularly in robotics and autonomous systems.
• This approach enhances the efficiency and effectiveness of global optimization for complex, real-world problems.
• The method provides a robust solution for tackling nonstationary functions in black-box optimization settings.