FFT-Based Approximations for Black-Box Optimization

In this paper, we consider the problem of black-box function optimization. We propose an FFT-based algorithm that adaptively updates the parameters of a bandlimited Gaussian process surrogate model for the function. Our algorithm uses these parameters to construct approximate upper confidence bounds that determine its sampling behavior. We show that when the underlying function can be extended as a periodic function whose bandwidth is sufficiently small relative to the evaluation budget, our models converge to a perfect reconstruction, allowing our algorithm to recover the true optimizer. For periodic bandlimited function spaces, our algorithm has reduced complexity compared to traditional GP-UCB-based algorithms and demonstrates improved robustness.