Symmetry-Aware Bayesian Optimization via Max Kernels
This work addresses the challenge of optimizing noisy, expensive black-box functions with symmetries, offering a domain-specific improvement for Bayesian Optimization.
The paper tackled the problem of improving Bayesian Optimization efficiency for functions with symmetries by using a positive semidefinite projection of the max kernel, achieving significantly lower regret on synthetic and real-world benchmarks.
Bayesian Optimization (BO) is a powerful framework for optimizing noisy, expensive-to-evaluate black-box functions. When the objective exhibits invariances under a group action, exploiting these symmetries can substantially improve BO efficiency. While using maximum similarity across group orbits has long been considered in other domains, the fact that the max kernel is not positive semidefinite (PSD) has prevented its use in BO. In this work, we revisit this idea by considering a PSD projection of the max kernel. Compared to existing invariant (and non-invariant) kernels, we show it achieves significantly lower regret on both synthetic and real-world BO benchmarks, without increasing computational complexity.