Boundary Exploration for Bayesian Optimization With Unknown Physical Constraints
This addresses the challenge of optimizing functions with unknown constraints in real-world applications like engineering design, though it is an incremental improvement over existing Bayesian optimization methods.
The paper tackles the problem of optimizing black-box functions with unknown physical constraints, where optimal solutions often lie on the boundary between feasible and infeasible regions, and proposes BE-CBO, a Bayesian optimization method that efficiently explores this boundary using an ensemble of neural networks, demonstrating superior performance against state-of-the-art methods in experiments.
Bayesian optimization has been successfully applied to optimize black-box functions where the number of evaluations is severely limited. However, in many real-world applications, it is hard or impossible to know in advance which designs are feasible due to some physical or system limitations. These issues lead to an even more challenging problem of optimizing an unknown function with unknown constraints. In this paper, we observe that in such scenarios optimal solution typically lies on the boundary between feasible and infeasible regions of the design space, making it considerably more difficult than that with interior optima. Inspired by this observation, we propose BE-CBO, a new Bayesian optimization method that efficiently explores the boundary between feasible and infeasible designs. To identify the boundary, we learn the constraints with an ensemble of neural networks that outperform the standard Gaussian Processes for capturing complex boundaries. Our method demonstrates superior performance against state-of-the-art methods through comprehensive experiments on synthetic and real-world benchmarks. Code available at: https://github.com/yunshengtian/BE-CBO