Overview
This work introduces KSOS-BO, a novel kernel-based, derivative-free framework designed to enhance the optimization of acquisition functions within the Bayesian Optimization (BO) paradigm. KSOS-BO reformulates the acquisition function optimization problem as a semidefinite program utilizing kernel-induced representations. This approach aims to achieve a structured global search during the sampling phase of BO.
Research Context
Bayesian Optimization (BO) is an established framework for global optimization, particularly effective for functions characterized by expensive evaluations. Its utility extends to functions defined over continuous domains and those involving stochastic noise in evaluations. BO is widely applied in various fields requiring sample efficiency, such as hyperparameter tuning, robotics policy search, and scientific experiment design. The typical BO procedure involves two main steps: model fitting, followed by the optimization of an acquisition function. This latter step, the optimization of the acquisition function, is often treated as a generic black-box problem, despite its inherent structural properties.
Approach
The KSOS-BO framework addresses the acquisition function optimization in BO by framing it as a semidefinite program. This formulation leverages kernel-induced representations. This structured approach to the optimization of the acquisition function departs from generic black-box optimization methods previously employed. The methodology is derivative-free, indicating that it does not rely on gradient information during its optimization process.
Findings
Across a diverse set of benchmark functions, characterized by varying landscape properties, KSOS-BO demonstrated consistent performance improvements over existing derivative-free baselines. These baselines included methods such as Sobol Search, Differential Evolution, and CMA-ES for acquisition function optimization. KSOS-BO achieved an average regret improvement of 81.16% on 10 out of 15 benchmarks. The framework exhibited strong performance specifically on highly multimodal functions and unimodal functions that were ill-conditioned, suggesting its applicability across different landscape structures.
In terms of computational efficiency, KSOS-BO displayed a faster convergence in wall-clock time, with an average improvement of 93.55% on 10 out of 15 benchmarks. This faster convergence was attributed to its ability to reach high-quality solutions with fewer evaluations, despite having a higher per-iteration computational cost.
Key Limitations Mentioned by Researchers
The researchers noted specific limitations for KSOS-BO, including reduced effectiveness when applied to functions containing steep drops or plate-shaped regions.
Potential Applications
- Global optimization of functions with expensive evaluations
- Hyperparameter tuning in machine learning
- Robotics policy search
- Design of scientific experiments