Adaptive and Safe Bayesian Optimization in High Dimensions via One-Dimensional Subspaces
This work addresses the scalability and safety issues in Bayesian optimization for high-dimensional settings, such as in scientific applications like free-electron lasers, though it is incremental as it builds on existing subspace and safe optimization methods.
The authors tackled the challenge of scaling Bayesian optimization to high dimensions by proposing LineBO, which restricts optimization to iteratively chosen one-dimensional subspaces, achieving competitive performance on synthetic benchmarks and successfully optimizing a 40-parameter beam intensity problem with safety constraints.
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.