Neural-BO: A Black-box Optimization Algorithm using Deep Neural Networks (2303.01682v3)

Abstract: Bayesian Optimization (BO) is an effective approach for global optimization of black-box functions when function evaluations are expensive. Most prior works use Gaussian processes to model the black-box function, however, the use of kernels in Gaussian processes leads to two problems: first, the kernel-based methods scale poorly with the number of data points and second, kernel methods are usually not effective on complex structured high dimensional data due to curse of dimensionality. Therefore, we propose a novel black-box optimization algorithm where the black-box function is modeled using a neural network. Our algorithm does not need a Bayesian neural network to estimate predictive uncertainty and is therefore computationally favorable. We analyze the theoretical behavior of our algorithm in terms of regret bound using advances in NTK theory showing its efficient convergence. We perform experiments with both synthetic and real-world optimization tasks and show that our algorithm is more sample efficient compared to existing methods.