Adaptive and Safe Bayesian Optimization in High Dimensions via One-Dimensional Subspaces

TL;DR

This paper introduces LineBO, a scalable Bayesian optimization method that reduces high-dimensional problems to one-dimensional sub-problems, ensuring safety and efficiency, with theoretical guarantees and practical success in complex applications.

Contribution

The paper proposes LineBO, a novel high-dimensional Bayesian optimization algorithm that automatically adapts to effective subspaces and guarantees safety, combining theoretical analysis with real-world application.

Findings

Global convergence of LineBO demonstrated

Fast local convergence for strongly convex functions

Successful optimization of Swiss Free Electron Laser parameters

Abstract

Bayesian optimization is known to be difficult to scale to high dimensions, because the acquisition step requires solving a non-convex optimization problem in the same search space. In order to scale the method and keep its benefits, we propose an algorithm (LineBO) that restricts the problem to a sequence of iteratively chosen one-dimensional sub-problems that can be solved efficiently. We show that our algorithm converges globally and obtains a fast local rate when the function is strongly convex. Further, if the objective has an invariant subspace, our method automatically adapts to the effective dimension without changing the algorithm. When combined with the SafeOpt algorithm to solve the sub-problems, we obtain the first safe Bayesian optimization algorithm with theoretical guarantees applicable in high-dimensional settings. We evaluate our method on multiple synthetic benchmarks, where we obtain competitive performance. Further, we deploy our algorithm to optimize the beam intensity of the Swiss Free Electron Laser with up to 40 parameters while satisfying safe operation constraints.