Bayesian Optimization over Bounded Domains with the Beta Product Kernel
This work addresses a domain-specific problem in Bayesian optimization for researchers and practitioners dealing with bounded domains, offering an incremental improvement over existing kernels.
The paper tackled the limitation of standard Gaussian process kernels in Bayesian optimization for bounded domains by introducing the Beta kernel, which models functions on bounded domains and consistently outperformed existing kernels like Matérn and RBF in synthetic and real-world tasks such as model compression.
Bayesian optimization with Gaussian processes (GP) is commonly used to optimize black-box functions. The Matérn and the Radial Basis Function (RBF) covariance functions are used frequently, but they do not make any assumptions about the domain of the function, which may limit their applicability in bounded domains. To address the limitation, we introduce the Beta kernel, a non-stationary kernel induced by a product of Beta distribution density functions. Such a formulation allows our kernel to naturally model functions on bounded domains. We present statistical evidence supporting the hypothesis that the kernel exhibits an exponential eigendecay rate, based on empirical analyses of its spectral properties across different settings. Our experimental results demonstrate the robustness of the Beta kernel in modeling functions with optima located near the faces or vertices of the unit hypercube. The experiments show that our kernel consistently outperforms a wide range of kernels, including the well-known Matérn and RBF, in different problems, including synthetic function optimization and the compression of vision and language models.